College Physics 9e

1 Introduction ANSWERS TO MULTIPLE CHOICE QUESTIONS 1. Using a calculator to augment the diffusiveness by the width communicates a exposed defense of 6783 m 2 , referablewithstanding this defense must be rounded to embcareer the selfselfidentical reckon of tokeni? lingo ? gures as the decisive deferential constituent in the emanation. The decisive deferential constituent is the diffusiveness, which embraces either 2 or 3 tokeni? lingo ? gures, halting on whether the luxuriance naught is tokeni? lingo or is nature explanationd simply to establish the decimal purpose. Incorporateptuous the diffusiveness embraces 3 tokeni? lingo ? gures, defense (c) truly expresses the area as 6. 78 ? 10 3 m 2 .
However, if the diffusiveness embraces simply 2 tokeni? lingo ? gures, defense (d) communicates the set-rectilinear development as 6. 8 ? 10 3 m 2 . Twain defenses (d) and (e) could be physically meaningful. Defenses (a), (b), and (c) must be meaninghither gundisconnected quantities can be inferuddy or withdrawed simply if they keep the selfselfidentical quantity. According to Newton’s succor decree, Cece = heap ? succor . Thus, the aces of Cece must be the emanation of the aces of heap (kg) and the aces of succor ( m s 2 ). This resigns kg ? m s 2, which is defense (a). The calculator communicates an defense of 57. 573 ce the validity of the 4 absorbed reckons.
However, this validity must be rounded to 58 as absorbed in defense (d) so the reckon of decimal assigns in the development is the selfselfidentical (zero) as the reckon of decimal assigns in the integer 15 (the adorderly in the validity embraceing the meanest reckon of decimal assigns). The exactd disagree is absorbed by: ? 1 000 mm ? ? 1. 00 cubitus ? h = ( 2. 00 m ) ? ?? ? = 4. 49 cubiti ? 1. 00 m ? ? 445 mm ? This development corresponds to defense (c). 6. The absorbed area (1 420 ft 2 ) embraces 3 tokeni? lingo ? gures, incorporateptuous that the luxuriance naught is explanationd simply to establish the decimal purpose. The disagree of this admonish to clear meters is absorbed by: 1. 00 m ? 2 2 2 A = (1. 2 ? 10 3 ft 2 ) ? ? ? = 1. 32 ? 10 m = 132 m ? 3. 281 ft ? Referablee that the development embraces 3 tokeni? lingo ? gures, the selfselfidentical as the reckon of tokeni? lingo ? gures in the decisive deferential constituent explanationd in the circumspection. This development contestes defense (b). 7. You canreferpotent infer, withdraw, or equate a reckon apples and a reckon of days. Thus, the defense is yes ce (a), (c), and (e). Thus-far, you can augment or ceeveryot a reckon of apples and a reckon of days. Ce stance, you ability ceeveryot the reckon of apples by a reckon of days to ? nd the reckon of apples you could munch per day. In validitymary, the defenses are (a) yes, (b) no, (c) yes, (d) no, and (e) es. 2 2. 3. 4. 5. 1 http://helpyoustudy. info 2 Chapter 1 8. The absorbed Cartesian coordinates are x = ? 5. 00, and y = 12. 00 , with the decisive deferential embraceing 3 tokeni? lingo ? gures. Referablee that the speci? ed purpose (with x < 0 and y > 0 ) is in the succor quadrant. The disagree to polar coordinates is then absorbed by: r = x 2 + y 2 = ( ? 5. 00 ) + (12. 00 ) = 13. 0 2 2 tan ? = y 12. 00 = = ? 2. 40 x ? 5. 00 and ? = tan ? 1 ( ? 2. 40 ) = ? 67. 3° + 180° = 113° Referablee that 180° was inferuddy in the decisive tramp to retoken a succor quadrant disposition. The set-rectilinear defense is accordingly (b) (13. 0, 113°). 9. Doing measuremental dissection on the ? st 4 absorbed daintys resigns: (a) [ v] ?t ? ? ? 2 = LT L = 3 T2 T (b) [ v] ?x2 ? ? ? = LT = L? 1T ? 1 L2 (c) ? v 2 ? ( L T )2 L2 T 2 L2 ? ?= = = 3 T T T [t ] (d) ? v 2 ? ( L T )2 L2 T 2 L ? ?= = = 2 L L T [ x] Gundisconnected succor has aces of diffusiveness ceeveryotd by opportunity cleard, it is experiencen that the kinsman absorbed in defense (d) is congruous with an indication resigning a admonish ce succor. 10. The reckon of gallons of gasosuccession she can lapse is # gallons = incorpoadmonish disbursement 33 Euros ? exact per gallon ? Euros ? ? 1 L ? ? ? 1. 5 ?? L ? ? 1 quart ? ? ? ? ? 5 gal ? 4 quarts ? ? 1 gal ? ? ? ? ? so the set-rectilinear defense is (b). 1. The standing vivid is demonstrationn in the delineation at the rectilinear. h From this, remark that tan 26° = , or 45 m h = ( 45 m ) tan 26° = 22 m 26 h Thus, the set-rectilinear defense is (a). 12. 45 m Referablee that we may transcribe 1. 365 248 0 ? 10 7 as 136. 524 80 ? 10 5. Thus, the exposed defense, including the doubt, is x = (136. 524 80 ± 2) ? 10 5. Gundisconnected the ? nal defense should embcareer ceentire the digits we are firm of and undisconnected admiruddy digit, this development should be rounded and displayed as 137 ? 10 5 = 1. 37 ? 10 7 (we are firm of the 1 and the 3, referablewithstanding keep doubt abquenched the 7). We experience that this defense has three tokeni? lingo ? ures and dainty (d) is set-right. ANSWERS TO EVEN NUMBERED CONCEPTUAL QUESTIONS 2. Speckic clocks are buildationed on the electromagnetic waves that specks ceevert. As-well, pulsars are extremely recurrent astronomical clocks. http://helpyoustudy. info Introduction 3 4. (a) (b) (c) ~ 0. 5 lb ? 0. 25 kg or ~10 ? 1 kg ~ 4 lb ? 2 kg or ~10 0 kg ~ 4000 lb ? 2000 kg or ~10 3 kg 6. Let us affect the specks are valid circuits of transection 10? 10 m. Then, the compass of each speck is of the adorderly of 10? 30 m3. (Further clearly, compass = 4? r 3 3 = ? d 3 6 . ) Accordingly, gundisconnected 1 cm 3 = 10 ? 6 m 3, the reckon of specks in the 1 cm3 valid is on the adorderly of 10 ? 10 ? 30 = 10 24 specks. A further punctilious circumspection would exact conversance of the blindness of the valid and the heap of each speck. Thus-far, our admire agrees with the further punctilious circumspection to amid a constituent of 10. Realistically, the simply diffusivenesss you ability be potent to fulfill are the diffusiveness of a footbentire ? eld and the diffusiveness of a unpremeditatedspring? y. The simply opportunity interims matter to veri? cation would be the diffusiveness of a day and the opportunity betwixt customary heartbeats. In the metric method, aces dissent by powers of ten, so it’s very gentle and deferential to transform from undisconnected ace to another. 8. 10. ANSWERS TO EVEN NUMBERED PROBLEMS . 4. 6. 8. 10. 12. 14. 16. 18. (a) L T2 (b) L Ceentire three equations are measurementally faulty. (a) (a) (a) (a) (a) kg ? m s 22. 6 3. 00 ? 108 m s 346 m 2 ± 13 m 2 797 (b) (b) (b) (b) (b) Ft = p 22. 7 2 . 997 9 ? 108 m s 66. 0 m ± 1. 3 m 1. 1 (c) 17. 66 (c) (c) 22. 6 is further relipotent 2. 997 925 ? 108 m s 3. 09 cm s (a) (b) (c) (d) 5. 60 ? 10 2 km = 5. 60 ? 10 5 m = 5. 60 ? 10 7 cm 0. 491 2 km = 491. 2 m = 4. 912 ? 10 4 cm 6. 192 km = 6. 192 ? 10 3 m = 6. 192 ? 10 5 cm 2. 499 km = 2. 499 ? 10 3 m = 2. 499 ? 10 5 cm 20. 22. 24. 26. 10. 6 km L 9. 2 nm s 2 . 9 ? 10 2 m 3 = 2 . 9 ? 108 cm 3 2 . 57 ? 10 6 m 3 ttp://helpyoustudy. info 4 Chapter 1 28. 30. 32. 34. ? 108 tramps ~108 tribe with collecteds on any absorbed day (a) (a) 4. 2 ? 10 ? 18 m 3 ? 10 29 prokaryotes (b) (b) ~10 ? 1 m 3 ~1014 kg (c) ~1016 cells (c) The very abundant heap of prokaryotes implies they are essential to the biosphere. They are imperative ce ? xing carbon, conceding oxygen, and nonobservance up pollutants, inchoate multifarious other biological roles. Ethnicals halt on them! 36. 38. 40. 42. 44. 46. 48. 2. 2 m 8. 1 cm ? s = r12 + r22 ? 2r1r2 cos (? 1 ? ?2 ) 2. 33 m (a) 1. 50 m (b) 2. 60 m 8. 60 m (a) and (b) (c) 50. 52. 54. y= (a) y x = tan 12. 0°, y ( x ? . 00 km ) = tan 14. 0° d ? tan ? ? tan ? tan ? ? tan ? 1. 609 km h (b) 88 km h (d) 1. 44 ? 10 3 m (c) 16 km h Affects population of 300 favorite, medium of 1 can week per divorceicular, and 0. 5 oz per can. (a) ? 1010 cans yr 7. 14 ? 10 ? 2 gal s A2 A1 = 4 ? 10 2 yr (b) (b) (b) (b) ? 10 5 tons yr 2. 70 ? 10 ? 4 m 3 s V2 V1 = 8 ? 10 4 opportunitys (c) 1. 03 h 56. 58. 60. 62. (a) (a) (a) ? 10 4 globes yr. Affects 1 obsolete bentire per hitter, 10 hitters per inning, 9 innings per amusement, and 81 amusements per year. http://helpyoustudy. info Introduction 5 PROBLEM SOLUTIONS 1. 1 Substituting quantity into the absorbed equation T = 2? ionhither trustworthy, we keep g , and recognizing that 2? is a dimen- [T ] = [ ] [ g] or T= L = L T2 T2 = T Thus, the quantity are congruous . 1. 2 (a) From x = Bt2, we ? nd that B = [ B] = [ x] L = 2 [t 2 ] T x . Thus, B has aces of t2 (b) If x = A wickedness ( 2? ft ), then [ A] = [ x ] [wickedness ( 2? ft )] Referablewithstanding the wickednesse of an disstanding is a measurementhither pertinency. Accordingly, [ A] = [ x ] = L 1. 3 (a) The aces of compass, area, and elevation are: [V ] = L3, [ A] = L2 , and [h] = L We then remark that L3 = L2 L or [V ] = [ A][h] Thus, the equation V = Ah is measurementally set-rectilinear . (b) Vcylinder = ? R 2 h = (? R 2 ) h = Ah , where A = ?

R 2 Vrectangular punch = wh = ( w ) h = Ah, where A = w = diffusiveness ? width 1. 4 (a) L ML2 2 2 m v 2 = 1 m v0 + mgh, [ m v 2 ] = [ m v0 ] = M ? ? = 2 ? ? 2 T ? T? 1 2 L ? M L vocpotent ? mgh ? = M ? 2 ? L = . Thus, the equation is measurementally inset-rectilinear . ? ? ? T ? T ? In the equation 1 2 2 (b) L L referablewithstanding [at 2 ] = [a][t 2 ] = ? 2 ? ( T 2 ) = L. Hereafter, this equation ? ? T ? T ? is measurementally inset-rectilinear . In v = v0 + at 2, [ v] = [ v0 ] = L In the equation ma = v 2, we experience that [ ma] = [ m][a] = M ? 2 ? ?T Accordingly, this equation is as-well measurementally inset-rectilinear . 2 ? = ML , vocpotent [ v 2 ] = ? L ? = L . ? ? ? 2 T2 ? T ? T? 2 (c) . 5 From the comprehensive destroyer decree, the trustworthy G is G = Fr 2 Mm. Its aces are then [G ] = [ F ] ? r 2 ? ( kg ? m s2 ) ( m 2 ) m3 ? ?= = kg ? kg kg ? s 2 [ M ][ m ] http://helpyoustudy. info 6 Chapter 1 1. 6 (a) Solving KE = p2 ce the ceceum, p, communicates p = 2 m ( KE ) where the numeral 2 is a 2m measurementhither trustworthy. Measuremental dissection communicates the aces of ceceum as: [ p] = [ m ][ KE ] = M ( M ? L2 T 2 ) = M 2 ? L2 T 2 = M ( L T ) Accordingly, in the SI method, the aces of ceceum are kg ? ( m s ) . (b) Referablee that the aces of cece are kg ? m s 2 or [ F ] = M ? L T 2 . Then, remark that [ F ][ t ] = ( M ?
L T 2 ) ? T = M ( L T ) = [ p ] From this, it follows that cece multifarious by opportunity is proportional to ceceum: Ft = p . (Experience the sudden-thought–momentum theorem in Chapter 6, F ? ?t = ? p , which says that a trustworthy cece F multifarious by a vocpotent of opportunity ? t correspondents the disagree in ceceum, ? p. ) 1. 7 1. 8 Area = ( diffusiveness ) ? ( width ) = ( 9. 72 m )( 5. 3 m ) = 52 m 2 (a) Computing ( 8) 3 externally rounding the intervening development resigns ( 8) (b) 3 = 22. 6 to three tokeni? lingo ? gures. Rounding the intervening development to three tokeni? lingo ? gures resigns 8 = 2. 8284 > 2. 83 Then, we earn ( 8) 3 = ( 2. 83) = 22. 7 to three tokeni? ant ? gures. 3 (c) 1. 9 (a) (b) (c) (d) The defense 22. 6 is further relipotent owing rounding in bisect-among-incompact (b) was carried quenched so shortly. 78. 9 ± 0. 2 has 3 tokenifilingo figures with the doubt in the tenths standing. 3. 788 ? 10 9 has 4 tokenifilingo figures 2. 46 ? 10 ? 6 has 3 tokenifilingo figures 0. 003 2 = 3. 2 ? 10 ? 3 has 2 tokenifilingo figures . The span naughts were initiatoryly middle simply to standing the decimal. 1. 10 c = 2 . 997 924 58 ? 108 m s (a) (b) (c) Rounded to 3 tokeni? lingo ? gures: c = 3. 00 ? 108 m s Rounded to 5 tokeni? lingo ? gures: c = 2 . 997 9 ? 108 m s Rounded to 7 tokeni? lingo ? gures: c = 2 . 997 925 ? 08 m s 1. 11 Remark that the diffusiveness = 5. 62 cm, the width w = 6. 35 cm, and the elevation h = 2. 78 cm ceentire embcareer 3 tokeni? lingo ? gures. Thus, any emanation of these quantities should embcareer 3 tokeni? lingo ? gures. (a) (b) w = ( 5. 62 cm )( 6. 35 cm ) = 35. 7 cm 2 V = ( w ) h = ( 35. 7 cm 2 ) ( 2. 78 cm ) = 99. 2 cm 3 abided on contiguous page http://helpyoustudy. info Introduction 7 (c) wh = ( 6. 35 cm )( 2. 78 cm ) = 17. 7 cm 2 V = ( wh ) = (17. 7 cm 2 ) ( 5. 62 cm ) = 99. 5 cm 3 (d) In the rounding arrangement, smentire correspondentitys are either inferuddy to or withdrawed from an defense to fulfil the rules of tokeni? lingo ? gures.
Ce a absorbed rounding, dissentent smentire adjustments are made, introducing a regular correspondentity of randomness in the decisive tokeni? lingo digit of the ? nal defense. 2 2 2 A = ? r 2 = ? (10. 5 m ± 0. 2 m ) = ? ?(10. 5 m ) ± 2 (10. 5 m )( 0. 2 m ) + ( 0. 2 m ) ? ? ? 1. 12 (a) Recognize that the decisive adorderly in the brackets is insigni? lingo in alikeity to the other span. Thus, we keep A = ? ?110 m 2 ± 4. 2 m 2 ? = 346 m 2 ± 13 m 2 ? ? (b) 1. 13 C = 2? r = 2? (10. 5 m ± 0. 2 m ) = 66. 0 m ± 1. 3 m The decisive deferential measurement of the punch has span tokeni? lingo ? gures. Thus, the compass (emanation of the three quantity) achieve embcareer simply span tokeni? lingo ? ures. V = ? w ? h = ( 29 cm )(17. 8 cm )(11. 4 cm ) = 5. 9 ? 10 3 cm 3 1. 14 (a) The validity is rounded to 797 owing 756 in the adjusts to be inferuddy has no standings further the decimal. 0. 003 2 ? 356. 3 = ( 3. 2 ? 10 ? 3 ) ? 356. 3 = 1. 14016 must be rounded to 1. 1 owing 3. 2 ? 10 ? 3 has simply span tokeni? lingo ? gures. 5. 620 ? ? must be rounded to 17. 66 owing 5. 620 has simply disgusting tokeni? lingo ? gures. (b) (c) 1. 15 5 280 ft ? ? 1 probe ? 8 d = ( 250 000 mi ) ? ? ?? ? = 2 ? 10 probes ? 1. 000 mi ? ? 6 ft ? The defense is sconfused-talk to undisconnected tokeni? lingo ? gure owing of the rectifyness to which the disagree from probes to feet is absorbed. . 16 v= t = 186 furlongs 1 cetnight ? 1 cetnight ? ? 14 days ? ? ? 1 day ? ? 220 yds ?? ?? ? ? 8. 64 ? 10 4 s ? ? 1 furcovet ?? ?? ? ? 3 ft ?? ? ? 1 yd ?? ? ? 100 cm ? ?? ? ? 3. 281 ft ? ? ? giving v = 3. 09 cm s ? ? 3. 786 L ?? ? ? 1 gal ?? ? ? 10 3 cm 3 ? ? 1 m 3 ? = 0. 204 m 3 ?? ? ? 1 L ? ? 10 6 cm 3 ? ?? ? ? 1. 17 ? 9 gal 6. 00 firkins = 6. 00 firkins ? ? 1 firkin ? (a) 1. 18 1. 609 km ? 2 5 7 = ( 348 mi ) ? 6 ? ? = 5. 60 ? 10 km = 5. 60 ? 10 m = 5. 60 ? 10 cm ? 1. 000 mi ? ? 1. 609 km ? 4 h = (1 612 ft ) ? 2 ? = 0. 491 2 km = 491. 2 m = 4. 912 ? 10 cm 5 280 ft ? ? ? 1. 609 km ? 3 5 h = ( 20 320 ft ) ? = 6. 192 km = 6. 192 ? 10 m = 6. 192 ? 10 cm 5 280 ft ? ? (b) (c) abided on contiguous page http://helpyoustudy. info 8 Chapter 1 (d) ? 1. 609 km ? 3 5 d = (8 200 ft ) ? ? = 2 . 499 km = 2 . 499 ? 10 m = 2 . 499 ? 10 cm ? 5 280 ft ? In (a), the defense is sconfused-talk to three tokeni? lingo ? gures owing of the rectifyness of the initiatory postulates admonish, 348 miles. In (b), (c), and (d), the defenses are sconfused-talk to disgusting tokeni? lingo ? gures owing of the rectifyness to which the kilometers-to-feet disagree constituent is absorbed. 1. 19 v = 38. 0 m ? 1 km ? ? 1 mi ? ? 3 600 s ? ?? ? = 85. 0 mi h ?? ? s ? 10 3 m ? ? 1. 609 km ? 1 h ? Yes, the driver is strong the hurry stipulation by 10. 0 mi h . mi ? 1 km ? ? 1 gal ? ? = 10. 6 km L ?? ? gal ? 0. 621 mi ? ? 3. 786 L ? ? ? 1. 20 power = 25. 0 r= 1. 21 (a) (b) (c) transection 5. 36 in ? 2. 54 cm ? = ? ? = 6. 81 cm 2 2 ? 1 in ? 2 A = 4? r 2 = 4? ( 6. 81 cm ) = 5. 83 ? 10 2 cm 2 V= 4 3 4 3 ? r = ? ( 6. 81 cm ) = 1. 32 ? 10 3 cm 3 3 3 ? ? 1 h ? ? 2. 54 cm ? ? 10 9 nm ? ?? ? 3 600 s ? ? 1. 00 in ? ? 10 2 cm ? = 9. 2 nm s ? ?? ?? ?? 1. 22 ? 1 in ? ? 1 day admonish = ? ? 32 day ? ? 24 h ?? ? ?? This instrument that the proteins are assembled at a admonish of multifarious flakes of specks each succor! 1. 3 ? m ? ? 3 600 s ? ? 1 km ? ? 1 mi ? 8 c = ? 3. 00 ? 10 8 ?? ?? ?? ? = 6. 71 ? 10 mi h s ? ? 1 h ? ? 10 3 m ? ? 1. 609 km ? ? ? 2 . 832 ? 10 ? 2 m3 ? Compass of unpremeditatedspring = ( 50. 0 ft )( 26 ft )(8. 0 ft ) ? ? 1 ft 3 ? ? ? 100 cm ? = 2 . 9 ? 10 2 m3 = ( 2 . 9 ? 10 2 m3 ) ? = 2 . 9 ? 10 8 cm3 ? 1m ? ? 1. 25 1. 26 2 2 ? 1 m ? ?? 43 560 ft ? ? 1 m ? ? ?? ? = 3. 08 ? 10 4 m3 Compass = 25. 0 acre ft ? ? ? ? ? 3. 281 ft ? ?? 1 acre ? ? 3. 281 ft ? ? ? ? ? 1 Compass of pyramid = ( area of infamous )( elevation ) 3 3 1. 24 ( ) = 1 ? (13. 0 acres )( 43 560 ft 2 acre ) ? ( 481 ft ) = 9. 08 ? 10 7 f ? 3? ? 2 . 832 ? 10 ? 2 m3 ? 3 = ( 9. 08 ? 10 7 ft 3 ) ? 5 ? = 2 . 57 ? 10 m 1 ft3 ? ? 1. 27 Compass of cube = L 3 = 1 quart (Where L = diffusiveness of undisconnected roll of the cube. ) ? 1 gallon ? ? 3. 786 liter ? ? 1000 cm3 ? i = 947 cm3 Thus, L 3 = 1 quart ? ?? ? 4 quarts ? ? 1 gallon ? ? 1 liter ? ? ?? ? ? ( ) and L = 3 947 cm3 = 9. 82 cm http://helpyoustudy. info Introduction 9 1. 28 We admire that the diffusiveness of a tramp ce an medium divorceicular is abquenched 18 inches, or ruggedly 0. 5 m. Then, an admire ce the reckon of tramps exactd to rustication a boundlessness correspondent to the periphery of the Earth would be N= or 3 2? ( 6. 38 ? 10 6 m ) Periphery 2?
RE = ? ? 8 ? 10 7 tramps 0. 5 m tramp Tramp Diffusiveness Tramp Diffusiveness N ? 108 tramps 1. 29. We affect an medium respiration admonish of abquenched 10 breaths/minute and a customary vivacity p of 70 years. Then, an admire of the reckon of breaths an medium divorceicular would siege in a vivacityopportunity is ? ? breaths ? 10 7 ? min n = ? 10 ( 70 yr ) ? 3. 156 ? yr s ? ? 160 s ? = 4 ? 108 breaths ? ? ?? ? min ? 1 ? ? ?? ? or n ? 108 breaths 1. 30 We affect that the medium divorceicular lay-hold-ones a collected twice a year and is riling an medium of 7 days (or 1 week) each opportunity. Thus, on medium, each divorceicular is riling ce 2 weeks quenched of each year (52 weeks).
The approvelihood that a bisect-amongicular divorceicular achieve be riling at any absorbed opportunity correspondents the percentage of opportunity that divorceicular is riling, or approvelihood of rilingness = 2 weeks 1 = 52 weeks 26 The population of the Earth is closely 7 reckoningion. The reckon of tribe expected to keep a collected on any absorbed day is then 1 Reckon riling = ( population )( approvelihood of rilingness ) = ( 7 ? 10 9 ) ? ? = 3 ? 108 or ? 108 ( ? ? ? 26 ? 1. 31 (a) Affect that a customary intestinal confide has a diffusiveness of abquenched 7 m and medium transection of 4 cm. The admiruddy incorpoadmonish intestinal compass is then ? ?d 2 ? ? ( 0. 04 m ) Vincorpoadmonish = A = ? ( 7 m ) = 0. 009 m 3 ? 4 ? 4 ? 2 The bclassify compass shackled by a wickednessgle bacterium is Vbacteria ? ( customary diffusiveness flake ) = (10 ? 6 m ) = 10 ? 18 m 3 3 3 If it is affectd that bacteria hold undisconnected hundredth of the incorpoadmonish intestinal compass, the admire of the reckon of microorganisms in the ethnical intestinal confide is n= (b) 3 Vincorpoadmonish 100 ( 0. 009 m ) 100 = = 9 ? 1013 or n ? 1014 10 ? 18 m 3 Vbacteria The abundant admonish of the reckon of bacteria admiruddy to repose in the intestinal confide instrument that they are probably referpotent hazardous. Intestinal bacteria aid dispose prop and stipulate essential nutrients. Ethnicals and bacteria possess a mutually bene? ial symbiotic kinsmanship. Vcell = 3 4 3 4 ? r = ? (1. 0 ? 10 ? 6 m ) = 4. 2 ? 10 ? 18 m 3 3 3 1. 32 (a) (b) Consider your whole to be a cylinder having a radius of abquenched 6 inches (or 0. 15 m) and a elevation of abquenched 1. 5 meters. Then, its compass is Vwhole = Ah = (? r 2 ) h = ? ( 0. 15 m ) (1. 5 m ) = 0. 11 m 3 or ? 10 ? 1 m 3 2 abided on contiguous page http://helpyoustudy. info 10 Chapter 1 (c) The admire of the reckon of cells in the whole is then n= Vwhole Vcell = 0. 11 m 3 = 2. 6 ? 1016 or ? 1016 ? 18 3 4. 2 ? 10 m 1. 33 A reasonpotent imagine ce the transection of a weary ability be 3 ft, with a periphery (C = 2? r = ?
D = boundlessness rustications per alternation) of abquenched 9 ft. Thus, the incorpoadmonish reckon of alternations the weary ability mould is n= incorpoadmonish boundlessness rusticationed ( 50 000 mi )( 5 280 ft mi ) = 3 ? 10 7 rev, or ~ 10 7 rev = boundlessness per alternation 9 ft rev 1. 34 Defenses to this sum achieve disagree, reposeing on the impudences undisconnected moulds. This reresolution affects that bacteria and other prokaryotes hold closely undisconnected ten-millionth (10? 7) of the Earth’s compass, and that the blindness of a prokaryote, approve the blindness of the ethnical whole, is closely correspondent to that of soak (103 kg/m3). (a) admiruddy reckon = n = Vincorpoadmonish Vspecific prokaryote 10 )V ? ?7 Earth Vspecific prokaryote (10 )(10 m ) ? ? (diffusiveness flake) (10 m ) ?7 3 Earth ? 7 6 3 ? 6 3 (10 ) R 3 ? 10 29 (b) (c) 3 kg ? ? ? ? mincorpoadmonish = ( blindness )( incorpoadmonish compass) ? ?soak ? nVspecific ? = ? 10 3 3 ? (10 29 )(10 ? 6 m ) ? 1014 kg ? ? prokaryote ? ? m The very abundant heap of prokaryotes implies they are essential to the biosphere. They are imperative ce ? xing carbon, conceding oxygen, and nonobservance up pollutants, inchoate multifarious other biological roles. Ethnicals halt on them! x = r cos? = 2 . 5 m cos 35° = 2. 0 m 1. 35 The x coordinate is buildation as and the y coordinate ) y = r wickedness? = ( 2 . 5 m ) wickedness 35° = 1. m ( 2 1. 36 The x boundlessness quenched to the ? y is 2. 0 m and the y boundlessness up to the ? y is 1. 0 m. Thus, we can explanation the Pythagorean theorem to ? nd the boundlessness from the source to the ? y as d = x 2 + y2 = ( 2. 0 m ) + (1. 0 m ) 2 = 2. 2 m 1. 37 The boundlessness from the source to the ? y is r in polar coordinates, and this was buildation to be 2. 2 m in Sum 36. The disstanding ? is the disstanding betwixt r and the spirithither entireusion succession (the x axis in this subject). Thus, the disstanding can be buildation as tan ? = y 1. 0 m = = 0. 50 x 2. 0 m and ? = tan ? 1 ( 0. 50 ) = 27° The polar coordinates are r = 2. 2 m and ? = 27 ° 1. 8 The x boundlessness betwixt the span purposes is ? x = x2 ? x1 = ? 3. 0 cm ? 5. 0 cm = 8. 0 cm and the y boundlessness betwixt them is ? y = y2 ? y1 = 3. 0 cm ? 4. 0 cm = 1. 0 cm. The boundlessness betwixt them is buildation from the Pythagorean theorem: d= 1. 39 ? x + ? y = (8. 0 cm ) + (1. 0 cm ) = 2 2 2 2 65 cm 2 = 8. 1 cm Refer to the Figure absorbed in Sum 1. 40 underneath. The Cartesian coordinates ce the span absorbed purposes are: x1 = r1 cos ? 1 = ( 2. 00 m ) cos 50. 0° = 1. 29 m y1 = r1 wickedness ? 1 = ( 2. 00 m ) wickedness 50. 0° = 1. 53 m x2 = r2 cos ? 2 = ( 5. 00 m ) cos ( ? 50. 0°) = 3. 21 m y2 = r2 wickedness ? 2 = ( 5. 00 m ) wickedness ( ? 50. 0°) = ? 3. 3 m abided on contiguous page http://helpyoustudy. info Introduction 11 The boundlessness betwixt the span purposes is then: ? s = ( ? x ) + ( ? y ) = (1. 29 m ? 3. 21 m ) + (1. 53 m + 3. 83 m ) = 5. 69 m 2 2 2 2 1. 40 Consider the Figure demonstrationn at the rectilinear. The Cartesian coordinates ce the span purposes are: x1 = r1 cos ? 1 y1 = r1 wickedness ? 1 x2 = r2 cos ? 2 y2 = r2 wickedness ? 2 y (x1, y1) r1 ?s ?y y1 y2 The boundlessness betwixt the span purposes is the diffusiveness of the hypotenexplanation of the shaded tridisstanding and is absorbed by ? s = ( ? x ) + ( ? y ) = 2 2 q1 ( x1 ? x2 ) + ( y1 ? y2 ) 2 2 (x2, y2) r2 ? x q2 x1 x2 x or ? s = (r 2 1 cos 2 ? 1 + r22 cos 2 ? ? 2r1r2 cos ? 1 cos ? 2 ) + ( r12 wickedness 2 ? 1 + r22 wickedness 2 ? 2 ? 2r1r2 wickedness ? 1 wickedness ? 2 ) = r12 ( cos 2 ? 1 + wickedness 2 ? 1 ) + r22 ( cos 2 ? 2 + wickedness 2 ? 2 ) ? 2r1r2 ( cos ? 1 cos ? 2 + wickedness ? 1 wickedness ? 2 ) i Applying the identities cos 2 ? + wickedness 2 ? = 1 and cos ? 1 cos ? 2 + wickedness ? 1 wickedness ? 2 = cos (? 1 ? ?2 ) , this ruddyuces to ? s = r12 + r22 ? 2r1r2 ( cos ? 1 cos ? 2 + wickedness ? 1 wickedness ? 2 ) = 1. 41 (a) r12 + r22 ? 2r1r2 cos (? 1 ? ?2 ) With a = 6. 00 m and b nature span rolls of this rectilinear tridisstanding having hypotenexplanation c = 9. 00 m, the Pythagorean theorem communicates the hidden roll as b = c2 ? a2 = ( 9. 00 m )2 ? ( 6. 00 m )2 = 6. 1 m (c) wickedness ? = b 6. 71 m = = 0. 746 c 9. 00 m (b) tan ? = a 6. 00 m = = 0. 894 b 6. 71 m 1. 42 From the diagram, cos ( 75. 0°) = d L Thus, d = L cos ( 75. 0°) = ( 9. 00 m ) cos ( 75. 0°) = 2. 33 m L 9 . 00 m 75. 0 d http://helpyoustudy. info 12 Chapter 1 1. 43 The periphery of the rise is C = 2? r , so the radius is C 15. 0 m = = 2. 39 m 2? 2? h h Thus, tan ( 55. 0°) = = which communicates r 2. 39 m r= h = ( 2. 39 m ) tan ( 55. 0°) = 3. 41 m 1. 44 (a) (b) wickedness ? = cos ? = antagonistic roll so, antagonistic roll = ( 3. 00 m ) wickedness ( 30. 0° ) = 1. 50 m hypotenexplanation close roll so, close roll = ( 3. 00 m ) cos ( 30. ° ) = 2 . 60 m hypotenexplanation (b) (d) The roll close to ? = 3. 00 wickedness ? = 4. 00 = 0. 800 5. 00 1. 45 (a) (c) (e) The roll antagonistic ? = 3. 00 cos ? = tan ? = 4. 00 = 0. 800 5. 00 4. 00 = 1. 33 3. 00 1. 46 Using the diagram at the rectilinear, the Pythagorean theorem resigns c = ( 5. 00 m ) + ( 7. 00 m ) = 8. 60 m 2 2 5. 00 m c q 7. 00 m 1. 47 From the diagram absorbed in Sum 1. 46 aloft, it is experiencen that tan ? = 5. 00 = 0. 714 7. 00 and ? = tan ? 1 ( 0. 714 ) = 35. 5° 1. 48 (a) and (b) (c) Experience the Figure absorbed at the rectilinear. Applying the de? nition of the tangent business to the abundant rectilinear tridisstanding embraceing the 12. ° disstanding communicates: y x = tan 12. 0° [1] As-well, applying the de? nition of the tangent business to the feebleer rectilinear tridisstanding embraceing the 14. 0° disstanding communicates: y = tan 14. 0° x ? 1. 00 km (d) From Equation [1] aloft, remark that x = y tan 12. 0° [2] Substituting this development into Equation [2] communicates y ? tan 12. 0° = tan 14. 0° y ? (1. 00 km ) tan 12. 0° abided on contiguous page http://helpyoustudy. info Introduction 13 Then, solving ce the elevation of the mountain, y, resigns y= 1. 49 (1. 00 km ) tan 12. 0° tan 14. 0° tan 14. 0° ? tan 12. 0° = 1. 44 km = 1. 44 ? 10 3 m Using the outsequence at the rectilinear: w = tan 35. ° , or 100 m w = (100 m ) tan 35. 0° = 70. 0 m w 1. 50 The ? gure at the rectilinear demonstrations the standing vivid in the sum proposition. Applying the de? nition of the tangent business to the abundant rectilinear tridisstanding embraceing the disstanding ? in the Figure, undisconnected earns y x = tan ? As-well, applying the de? nition of the tangent business to the smentire rectilinear tridisstanding embraceing the disstanding ? communicates y = tan ? x? d Solving Equation [1] ce x and substituting the development into Equation [2] resigns y = tan ? y tan ? ? d The decisive development simpli? es to or y ? tan ? = tan ? y ? d ? tan ? y ? tan ? = y ? tan ? ? d ? tan ? ? tan ? or [2] [1]
Solving ce y: y ( tan ? ? tan ? ) = ? d ? tan ? ? tan ? y=? 1. 51 (a) d ? tan ? ? tan ? d ? tan ? ? tan ? = tan ? ? tan ? tan ? ? tan ? Absorbed that a ? F m , we keep F ? ma . Accordingly, the aces of cece are those of ma, [ F ] = [ ma] = [ m][a] = M ( L T 2 ) = M L T-2 (b) L M? L [F ] = M ? 2 ? = 2 ? ? T ? T ? 1 so newton = kg ? m s2 1. 52 (a) mi ? mi ? ? 1. 609 km ? km = ? 1 ?? ? = 1. 609 h ? h ? ? 1 mi ? h mi ? mi ? ? 1. 609 km h ? km = ? 55 ?? ? = 88 h ? h ? ? 1 mi h ? h mi mi ? mi ? ? 1. 609 km h ? km ? 55 = ? 10 ?? ? = 16 h h ? h ? ? 1 mi h ? h (b) vmax = 55 (c) ?vmax = 65 http://helpyoustudy. info 14 Chapter 1 1. 3 (a) Gundisconnected 1 m = 10 2 cm , then 1 m 3 = (1 m ) = (10 2 cm ) = (10 2 ) cm 3 = 10 6 cm 3, giving 3 3 3 ? 1. 0 ? 10 ? 3 kg ? 3 heap = blindness compass = ? ? 1. 0 m 3 ? 1. 0 cm ? ( )( ) ( ) ? 10 6 cm3 ? ? kg ? 3 = ? 1. 0 ? 10 ? 3 3 ? 1. 0 m 3 ? ? = 1. 0 ? 10 kg 3 ? cm ? ? 1m ? ( ) As a rugged circumspection, trmunch each of the cethcoming goals as if they were 100% soak. (b) (c) (d) 3 kg 4 cell: heap = blindness ? compass = ? 10 3 3 ? ? ( 0. 50 ? 10 ? 6 m ) = 5. 2 ? 10 ? 16 kg ? ? m ? 3 ? 3 4 kg 4 kidney: heap = blindness ? compass = ? ? ? r 3 ? = ? 10 3 3 ? ? ( 4. 0 ? 10 ? 2 m ) = 0. 27 kg ? ? ? ? m ? 3 ? 3 ? ? ?y: heap = blindness ? olume = ( blindness ) (? r 2 h ) 2 kg = ? 10 3 3 ? ? (1. 0 ? 10 ? 3 m ) ( 4. 0 ? 10 ? 3 m ) = 1. 3 ? 10 ? 5 kg ? ? m ? ? 1. 54 Affect an medium of 1 can per divorceicular each week and a population of 300 favorite. (a) reckon cans divorceicular ? reckon cans year = ? ? ? ( population )( weeks year ) week ? ? ? ?1 ? ? can divorceicular ? 8 ? ( 3 ? 10 tribe ) ( 52 weeks yr ) week ? ? 2 ? 1010 cans yr , or ~10 10 cans yr (b) reckon of tons = ( power can )( reckon cans year ) ? oz ? ? 1 lb ? ? 1 ton ?? ? 10 can ? ? ?? 0. 5 ? ?? ?? ?? ? 2 ? 10 ? can ? ? 16 oz ? ? 2 000 lb ?? ? yr ? ?? ? 3 ? 10 5 ton yr , or ~10 5 ton yr Affects an medium power of 0. oz of aluminum per can. 1. 55 The adorderly s has quantity of L, a has quantity of LT? 2, and t has quantity of T. Accordingly, the equation, s = k a m t n with k nature measurementless, has quantity of L = ( LT ? 2 ) ( T ) m n or L1T 0 = L m T n? 2 m The powers of L and T must be the selfselfidentical on each roll of the equation. Accordingly, L1 = Lm and m =1 Approvewise, equating powers of T, we experience that n ? 2 m = 0, or n = 2 m = 2 Measuremental dissection canreferpotent indicate the admonish of k , a measurementhither trustworthy. 1. 56 (a) The admonish of ? lling in gallons per succor is admonish = 30. 0 gal ? 1 min ? ?2 ? ? = 7. 14 ? 10 gal s 7. 0 min ? 60 s ? abided on contiguous page http://helpyoustudy. info Introduction 15 (b) 3 1L Referablee that 1 m 3 = (10 2 cm ) = (10 6 cm 3 ) ? 3 ? 3 ? 10 cm ? = 10 3 L. Thus, ? ? admonish = 7. 14 ? 10 ? 2 (c) t= gal ? 3. 786 L ? ? 1 m 3 ? ?4 3 ? ?? ? = 2. 70 ? 10 m s s ? 1 gal ? ? 10 3 L ? ? 1h ? Vfilled 1. 00 m 3 = = 3. 70 ? 10 3 s ? ? = 1. 03 h ? 4 3 admonish 2. 70 ? 10 m s ? 3 600 s ? 1. 57 The compass of color explanationd is absorbed by V = Ah, where A is the area dressed and h is the lumpishness of the flake. Thus, h= V 3. 79 ? 10 ? 3 m 3 = = 1. 52 ? 10 ? 4 m = 152 ? 10 ? 6 m = 152 ? m 25. 0 m 2 A 1. 58 (a) Ce a circuit, A = 4? R 2 .
In this subject, the radius of the succor circuit is twice that of the ? rst, or R2 = 2 R1. Hereafter, A2 4? R 2 R 2 ( 2 R1 ) 2 = = 2 = = 4 2 2 A1 4? R 1 R 1 R12 2 (b) Ce a circuit, the compass is Thus, V= 4 3 ? R 3 3 V2 ( 4 3) ? R 3 R 3 ( 2 R1 ) 2 = = 2 = = 8 3 3 3 V1 ( 4 3) ? R 1 R 1 R1 1. 59 The admire of the incorpoadmonish boundlessness cars are driven each year is d = ( cars in explanation ) ( boundlessness rusticationed per car ) = (100 ? 10 6 cars )(10 4 mi car ) = 1 ? 1012 mi At a admonish of 20 mi/gal, the fuel explanationd per year would be V1 = d 1 ? 1012 mi = = 5 ? 1010 gal admonish1 20 mi gal If the admonish acceptiond to 25 mi gal, the annual fuel decay would be V2 = d 1 ? 012 mi = = 4 ? 1010 gal admonish2 25 mi gal and the fuel savings each year would be savings = V1 ? V2 = 5 ? 1010 gal ? 4 ? 1010 gal = 1 ? 1010 gal 1. 60 (a) The correspondentity compensated per year would be dollars ? ? 8. 64 ? 10 4 s ? ? 365. 25 days ? 10 dollars annual correspondentity = ? 1 000 ? ?? ?? ? = 3. 16 ? 10 s ? ? 1. 00 day ? ? yr yr ? ? Accordingly, it would siege (b) 10 ? 10 12 dollars = 3 ? 10 2 yr, 3. 16 ? 10 10 dollars yr or ~10 2 yr The periphery of the Earth at the equator is C = 2? r = 2? 6. 378 ? 10 6 m = 4. 007 ? 10 7 m ( ) abided on contiguous page http://helpyoustudy. info 16 Chapter 1 The diffusiveness of undisconnected dollar reckoning is 0. 55 m, so the diffusiveness of ten trillion reckonings is m ? 12 12 = ? 0. 155 ? ? (10 ? 10 dollars ) = 1? 10 m. Thus, the ten trillion dollars would dollar ? ? surround the Earth 1 ? 1012 m n= = = 2 ? 10 4 , or ~10 4 opportunitys C 4. 007 ? 10 7 m 1. 61 (a) (b) ? 365. 2 days ? ? 8. 64 ? 10 4 s ? 1 yr = (1 yr ) ? = 3. 16 ? 10 7 s ?? ? ? ? 1 day ? 1 yr ? ? ? Consider a bisect of the exterior of the Moon which has an area of 1 m2 and a profoundness of 1 m. When ? lled with meteorites, each having a transection 10? 6 m, the reckon of meteorites acovet each behalf of this punch is n= diffusiveness of an behalf 1m = = 10 6 meteorite transection 10 ? 6 m The incorpoadmonish reckon of meteorites in the ? led punch is then N = n 3 = 10 6 3 = 10 18 At the admonish of 1 meteorite per succor, the opportunity to ? ll the punch is 1y ? = 3 ? 10 10 yr, or t = 1018 s = (1018 s ) ? ? ? 7 ? 3. 16 ? 10 s ? 1. 62 ~1010 yr ( ) We achieve affect that, on medium, 1 bentire achieve be obsolete per hitter, that there achieve be abquenched 10 hitters per inning, a amusement has 9 innings, and the team plays 81 abode amusements per suitableness. Our admire of the reckon of amusement globes needed per suitableness is then reckon of globes needed = ( reckon obsolete per hitter ) ( reckon hitters/amusement )( abode amusements/year ) ?? amusements ? hitters ? ? innings ?? ? = (1 bentire per hitter ) ?? 10 ?? ? 81 ? ? ? year ? inning ? ? amusement ?? ? ?? = 7300 globes year or ~10 4 globes year 1. 63 The compass of the Milky Way bevy is ruggedly ? ?d2 ? ? VG = At = ? t ? 10 21 m 4 ? 4 ? ? ( ) (10 m ) 2 19 or VG ? 10 61 m3 r If, amid the Milky Way bevy, there is customaryly undisconnected neutron referpotent attributpotent attributpotent attributpotent attributpotent attributpotent attributpotent attributpotent attributableability in a round compass of radius r = 3 ? 1018 m, then the galactic compass per neutron referpotent attributpotent attributpotent attributpotent attributpotent attributpotent attributpotent attributpotent attributableability is V1 = 3 4 3 4 ? r = ? ( 3 ? 1018 m ) = 1 ? 10 56 m 3 3 3 or V1 ? 10 56 m 3 The adorderly of majority of the reckon of neutron referpotent attributpotent attributpotent attributpotent attributpotent attributpotent attributpotent attributpotent attributableabilitys in the Milky Way is then n= VG 10 61 m 3 ? V1 10 56 m 3 or n ? 10 5 neutron referpotent attributpotent attributpotent attributpotent attributpotent attributpotent attributpotent attributpotent attributableabilitys http://helpyoustudy. info 2 Agitation in Undisconnected Measurement
QUICK QUIZZES 1. 2. (a) (a) 200 yd (b) 0 (c) 0 Mock. The car may be inactiveing down, so that the inclination of its succor is antagonistic the inclination of its quickness. Penny. If the quickness is in the inclination clarified as disclaiming, a balancebearing succor causes a ruddyuce in hurry. Penny. Ce an accelerating bisect-amongicle to seal at ceevery, the quickness and succor must keep antagonistic tokens, so that the hurry is decreasing. If this is the subject, the bisect-amongicle achieve referpotent attributpotent attributpotent attributpotent attributpotent attributpotent attributpotent attributpotent attributablewithstanding conclude to repose. If the succor recrement trustworthy, thus-far, the bisect-amongicle must prepare to provoke intermittently, antagonistic to the inclination of its initiatory quickness.
If the bisect-amongicle concludes to repose and then stays at repose, the succor has beconclude naught at the cece the agitation seals. This is the subject ce a braking car—the succor is disclaiming and goes to naught as the car concludes to repose. (b) (c) 3. The quickness-vs. -opportunity graph (a) has a trustworthy arise, indicating a trustworthy succor, which is represented by the succor-vs. -opportunity graph (e). Graph (b) represents an goal whose hurry regularly acceptions, and does so at an ceforever increasing admonish. Thus, the succor must be increasing, and the succor-vs. -opportunity graph that best indicates this deportment is (d).
Graph (c) depicts an goal which ? rst has a quickness that acceptions at a trustworthy admonish, which instrument that the goal’s succor is trustworthy. The agitation then disagrees to undisconnected at trustworthy hurry, indicating that the succor of the goal beseems naught. Thus, the best contest to this standing is graph (f). 4. Dainty (b). According to graph b, there are some minutes in opportunity when the goal is concurrently at span dissentent x-coordinates. This is physically unusable. (a) The cerulean graph of Figure 2. 14b best demonstrations the pigmy’s standing as a business of opportunity. As experiencen in Figure 2. 4a, the boundlessness the pigmy has rusticationed grows at an increasing admonish ce closely three opportunity interims, grows at a equpotent admonish ce abquenched disgusting opportunity interims, and then grows at a powerhither admonish ce the decisive span interims. The ruddy graph of Figure 2. 14c best illustrates the hurry (boundlessness rusticationed per opportunity interim) of the pigmy as a business of opportunity. It demonstrations the pigmy shapeing hurry ce closely three opportunity interims, affecting at trustworthy hurry ce abquenched disgusting opportunity interims, then inactiveing to repose during the decisive span interims. 5. (b) 17 http://helpyoustudy. info 18 Chapter 2 (c) The bald graph of Figure 2. 4d best demonstrations the pigmy’s succor as a business of opportunity. The pigmy shapes quickness (overbearing succor) ce closely three opportunity interims, provokes at trustworthy quickness (naught succor) ce abquenched disgusting opportunity interims, and then loses quickness (disclaiming succor) ce ruggedly the decisive span opportunity interims. 6. Dainty (e). The succor of the bentire recrement trustworthy vocpotent it is in the principle. The majority of its succor is the uncounted-fentire succor, g = 9. 80 m/s2. Dainty (c). As it rustications upward, its hurry ruddyuces by 9. 80 m/s during each succor of its agitation. When it reaches the peak of its agitation, its hurry beseems naught.
As the bentire provokes downward, its hurry acceptions by 9. 80 m/s each succor. Daintys (a) and (f). The ? rst jumper achieve regularly be affecting with a remarkpotent quickness than the succor. Thus, in a absorbed opportunity interim, the ? rst jumper covers further boundlessness than the succor, and the disengagement boundlessness betwixt them acceptions. At any absorbed minute of opportunity, the velocities of the jumpers are de? nitely dissentent, owing undisconnected had a commander referpotent attributpotent attributpotent attributpotent attributpotent attributpotent attributpotent attributpotent attributableabilityt. In a opportunity interim following this minute, thus-far, each jumper acceptions his or her quickness by the selfselfidentical correspondentity, owing they keep the selfselfidentical succor. Thus, the dissentence in velocities stays the selfsame. . 8. ANSWERS TO MULTIPLE CHOICE QUESTIONS 1. Once the arrow has left the bend, it has a trustworthy downward succor correspondent to the uncountedfentire succor, g. Prelude upward as the balancebearing inclination, the late opportunity exactd ce the quickness to disagree from an judicious admonish of 15. 0 m s upward ( v0 = +15. 0 m s ) to a admonish of 8. 00 m s downward ( v f = ? 8. 00 m s ) is absorbed by ? t = ? v v f ? v0 ? 8. 00 m s ? ( +15. 0 m s ) = = = 2. 35 s a ? g ? 9. 80 m s 2 Thus, the set-rectilinear dainty is (d). 2. In Figure MCQ2. 2, there are ? ve boundlessnesss separating close levigate drops, and these boundlessnesss p a boundlessness of ? x = 600 meters.
Gundisconnected the drops take-assign ceentire 5. 0 s, the opportunity p of each boundlessness is 5. 0 s and the incorpoadmonish opportunity interim demonstrationn in the ? gure is ? t = 5 ( 5. 0 s ) = 25 s. The medium hurry of the car is then v= ? x 600 m = = 24 m s ? t 25 s making (b) the set-rectilinear dainty. 3. The cause of the equations of kinematics ce an goal affecting in undisconnected measurement (Equations 2. 6 thrugged 2. 10 in the textbook) was buildationed on the impudence that the goal had a trustworthy succor. Thus, (b) is the set-rectilinear defense. An goal having trustworthy succor would keep trustworthy quickness simply if that succor had a admonish of naught, so (a) is referpotent a inevitpotent mode.
The hurry (majority of the quickness) achieve acception in opportunity simply in subjects when the quickness is in the selfselfidentical inclination as the trustworthy succor, so (c) is referpotent a set-rectilinear defense. An goal inexhaustive rectilinear upward into the principle has a trustworthy succor. Yet its standing (altitude) does referpotent regularly acception in opportunity (it referpotent attributpotent attributpotent attributpotent attributpotent attributpotent attributpotent attributpotent attributablewithstanding referpotent attributpotent attributpotent attributpotent attributpotent attributpotent attributpotent attributpotent attributableabilityts to fentire tail downward) nor is its quickness regularly directed downward (the inclination of the trustworthy succor). Thus, neither (d) nor (e) can be set-right. http://helpyoustudy. info Agitation in Undisconnected Measurement 19 4. The bendling trifle has a trustworthy downward succor ( a = ? g = ? 9. 80 m s 2 ) vocpotent in ? ght. The quickness of the trifle is directed upward on the upward bisect-among-incompact of its ? ight and is directed downward as it declines tail inparty the juggler’s workman. Thus, simply (d) is a penny proposition. The judicious quickness of the car is v0 = 0 and the quickness at opportunity t is v. The trustworthy succor is accordingly absorbed by a = ? v ? t = ( v ? v0 ) t = ( v ? 0 ) t = v t and the medium quickness of the car is v = ( v + v0 ) 2 = ( v + 0 ) 2 = v 2. The boundlessness rusticationed in opportunity t is ? x = vt = vt 2. In the divorceicular subject where a = 0 ( and hererearwards v = v0 = 0 ) , we experience that propositions (a), (b), (c), and (d) are ceentire set-right. Thus-far, in the public subject ( a ? , and hererearwards v ? 0 ), simply propositions (b) and (c) are penny. Propose (e) is referpotent penny in either subject. The agitation of the boat is very alike to that of a goal thrown rectilinear upward into the principle. In twain subjects, the goal has a trustworthy succor which is directed antagonistic to the inclination of the judicious quickness. Ordainly as the goal thrown upward inactives down and seals cecearily precedently it referpotent attributpotent attributpotent attributpotent attributpotent attributpotent attributpotent attributpotent attributableabilityts hurrying up as it declines tail downward, the boat achieve abide to provoke northward ce some opportunity, inactiveing once until it concludes to a ceceary seal. It achieve then referpotent attributpotent attributpotent attributpotent attributpotent attributpotent attributpotent attributpotent attributableabilityt to provoke in the southward inclination, shapeing hurry as it goes.
The set-rectilinear defense is (c). In a standing versus opportunity graph, the quickness of the goal at any purpose in opportunity is the arise of the succession tangent to the graph at that minute in opportunity. The hurry of the bisect-amongicle at this purpose in opportunity is simply the majority (or despotic admonish) of the quickness at this minute in opportunity. The misinterpretation take-placering during a opportunity interim is correspondent to the dissentence in x-coordinates at the ? nal and judicious opportunitys of the interim ? x = x t f ? x ti . 5. 6. 7. ( ) The medium quickness during a opportunity interim is the arise of the rectilinear succession connecting the purposes on the flexion selfcorresponding to the judicious and ? al opportunitys of the interim ? v = ? x ? t = ( x f ? xi ) ( t f ? ti ) ? . Thus, we experience how the quantities in daintys (a), (e), (c), and (d) ? ? can ceentire be earned from the graph. Simply the succor, dainty (b), canreferpotent be earned from the standing versus opportunity graph. 8. From ? x = v0 t + 1 at 2, the boundlessness rusticationed in opportunity t, referpotent attributpotent attributpotent attributpotent attributpotent attributpotent attributpotent attributpotent attributableabilityting from repose ( v0 = 0 ) with trustworthy 2 succor a, is ? x = 1 at 2 . Thus, the pertinency of the boundlessnesss rusticationed in span specific trials, undisconnected 2 of vocpotent t1 = 6 s and the succor of vocpotent t 2 = 2 s, is 2 2 ? x2 1 at 2 ? t 2 ? ? 2 s ? 1 2 = 1 2 =? ? =? ? = ? x1 2 at1 ? 1 ? ? 6 s ? 9 and the set-rectilinear defense is (c). 2 9. The boundlessness an goal affecting at a unvarying hurry of v = 8. 5 m s achieve rustication during a opportunity interim of ? t = 1 1 000 s = 1. 0 ? 10 ? 3 s is absorbed by ? x = v ( ? t ) = (8. 5 m s ) (1. 0 ? 10 ? 3 s ) = 8. 5 ? 10 ? 3 m = 8. 5 mm so the simply set-rectilinear defense to this scrutiny is dainty (d). 10. Once either bentire has left the student’s workman, it is a voluntarily declineing whole with a trustworthy succor a = ? g (prelude upward as balancebearing). Accordingly, dainty (e) canreferpotent be penny. The judicious velocities of the ruddy and cerulean globes are absorbed by viR = + v0 and viB = ? 0 , respectively. The quickness of either bentire when it has a misinterpretation from the propel purpose of ? y = ? h (where h is the elevation of the construction) is buildation from v 2 = vi2 + 2a ( ? y ) as follows: 2 vR = ? viR + 2a ( ? y ) R = ? ( + v0 ) 2 + 2 ( ? g ) ( ? h ) = ? 2 v0 + 2 gh http://helpyoustudy. info 20 Chapter 2 and 2 vB = ? viB + 2a ( ? y ) B = ? ( ? v0 ) 2 + 2 ( ? g ) ( ? h ) = ? 2 v0 + 2 gh Referablee that the disclaiming token was clarified ce the innate in twain subjects gundisconnected each bentire is affecting in the downward inclination rectilinearway precedently it reaches the buildation.
From this, we experience that dainty (c) is penny. As-well, the hurrys of the span globes ordainly precedently hitting the buildation are 2 2 2 2 vR = ? v0 + 2 gh = v0 + 2 gh > v0 and vB = ? v0 + 2 gh = v0 + 2 gh > v0 Accordingly, vR = vB , so twain daintys (a) and (b) are mock. Thus-far, we experience that twain ? nal hurrys yield the judicious hurry and dainty (d) is penny. The set-rectilinear defense to this scrutiny is then (c) and (d). 11. At buildation resemblingize, the misinterpretation of the buffet from its propel purpose is ? y = ? h , where h is the 2 elevation of the uprise and upward has been clarified as the balancebearing inclination.
From v 2 = vo + 2a ( ? y ) , the hurry of the buffet ordainly precedently hitting the buildation is buildation to be 2 2 v = ± v0 + 2a ( ? y ) = v0 + 2 ( ? g ) ( ? h ) = (12 m s )2 + 2 ( 9. 8 m s2 ) ( 40. 0 m ) = 30 m s Dainty (b) is accordingly the set-rectilinear defense to this scrutiny. 12. Once the bentire has left the thrower’s workman, it is a voluntarily declineing whole with a trustworthy, non-zero, succor of a = ? g . Gundisconnected the succor of the bentire is referpotent naught at any purpose on its trajectory, daintys (a) thrugged (d) are ceentire mock and the set-rectilinear defense is (e). ANSWERS TO EVEN NUMBERED CONCEPTUAL QUESTIONS . Yes. The bisect-amongicle may seal at some minute, referablewithstanding peaceful keep an succor, as when a bentire thrown rectilinear up reaches its acme elevation. (a) (b) 6. (a) No. They can be explanationd simply when the succor is trustworthy. Yes. Naught is a trustworthy. In Figure (c), the visions are farther separately-incompact ce each successive opportunity interim. The goal is affecting inparty the rectilinear and hurrying up. This instrument that the succor is balancebearing in Figure (c). In Figure (a), the ? rst disgusting visions demonstration an increasing boundlessness rusticationed each opportunity interim and accordingly a balancebearing succor.
However, following the disgustingth vision, the spacing is decreasing, demonstrationing that the goal is now inactiveing down (or has disclaiming succor). In Figure (b), the visions are correspondently boundlessnessd, demonstrationing that the goal provoked the selfselfidentical boundlessness in each opportunity interim. Hereafter, the quickness is trustworthy in Figure (b). At the acme elevation, the bentire is cecearily at repose (i. e. , has naught quickness). The succor recrement trustworthy, with majority correspondent to the uncounted-fentire succor g and directed downward. Thus, flush though the quickness is cecearily naught, it abides to disagree, and the bentire achieve prepare to shape hurry in the downward inclination.
The succor of the bentire recrement trustworthy in majority and inclination throughquenched the globe’s uncounted ? ight, from the minute it leaves the workman until the minute ordainly precedently it strikes the 4. (b) (c) 8. (a) (b) http://helpyoustudy. info Agitation in Undisconnected Measurement 21 buildation. The succor is directed downward and has a majority correspondent to the uncountedfentire succor g. 10. (a) Successive visions on the ? lm achieve be disconnected by a trustworthy boundlessness if the bentire has trustworthy quickness. Referpotent attributpotent attributpotent attributpotent attributpotent attributpotent attributpotent attributpotent attributableabilityting at the rectilinear-most vision, the visions achieve be achieveting closer concomitantly as undisconnected provokes inparty the left.
Starting at the rectilinear-most vision, the visions achieve be achieveting farther separately-incompact as undisconnected provokes inparty the left. As undisconnected provokes from left to rectilinear, the globes achieve ? rst achieve farther separately-incompact in each successive vision, then closer concomitantly when the bentire prepares to inactive down. (b) (c) (d) ANSWERS TO EVEN NUMBERED PROBLEMS 2. 4. 6. (a) (a) (a) (d) 8. (a) (d) 10. 12. (a) (a) (d) 14. 16. (a) 2 ? 10 4 mi 10. 04 m s 5. 00 m s ? 3. 33 m s +4. 0 m s 0 2. 3 min L t1 2 L ( t1 + t 2 ) 1. 3 ? 10 2 s (b) 13 m (b) (b) 64 mi ? L t 2 (c) 0 (b) (b) (b) (e) (b) ? x 2 RE = 2. 4 7. 042 m s 1. 25 m s 0 ? 0. 50 m s (c) ? 1. 0 m s (c) ? 2. 50 m s a) The luxuriance runner’s hurry must be superior than that of the director, and the director’s boundlessness from the ? nish succession must be grmunch abundance to communicate the luxuriance runner opportunity to mould up the de? cient boundlessness. (b) t = d ( v1 ? v2 ) (c) d2 = v2 d ( v1 ? v2 ) 18. (a) Some postulates purposes that can be explanationd to concoct the graph are as absorbed underneath: x (m) t (s) (b) (c) 5. 75 1. 00 16. 0 2. 00 35. 3 3. 00 68. 0 4. 00 119 5. 00 192 6. 00 41. 0 m s , 41. 0 m s , 41. 0 m s 17. 0 m s , abundantly feebleer than the minuteaneous quickness at t = 4. 00 s l http://helpyoustudy. info 22 Chapter 2 20. 22. 24. (a) 20. 0 m s , 5. 00 m s (b) 263 m 0. 91 s (i) (a) (ii) (a) 0 0 (b) (b) 1. 6 m s 2 1. 6 m s 2 500 x (m) (c) (c) 0. 80 m s 2 0 26. The flexions solidify at t = 16. 9 s. car police conductor 250 0 0 4. 00 8. 00 12. 0 16. 0 20. 0 t (s) 28. 30. a = 2. 74 ? 10 5 m s 2 = ( 2. 79 ? 10 4 ) g (a) (b) (e) 32. (a) (d) 34. 36. 38. 40. (a) (a) (a) (a) (c) 42. 44. 46. 48. 95 m 29. 1 s 1. 79 s v 2 = vi2 + 2a ( ? x ) f 8. 00 s 13. 5 m 22. 5 m 20. 0 s 5. 51 km 107 m v = a1t1 (c) a = ( v 2 ? vi2 ) 2 ( ? x ) f (d) 1. 25 m s 2 (b) 13. 5 m (c) 13. 5 m (b) (b) (b) (b) No, it canreferpotent fix safely on the 0. 800 km runway. 20. 8 m s, 41. 6 m s, 20. 8 m s, 38. 7 m s 1. 49 m s 2 ? = 1 a1t12 2 2 ? xincorpoadmonish = 1 a1t12 + a1t1t 2 + 1 a2 t 2 2 2 (a) Yes. (b) vtop = 3. 69 m s (c) ?v downward = 2. 39 m s (d) No, ? v upward = 3. 71 m s. The span buffets keep the selfselfidentical succor, referablewithstanding the buffet thrown downward has a remarkpotent medium hurry betwixt the span resemblingizes, and is ununresisting balance a feebleer opportunity interim. http://helpyoustudy. info Agitation in Undisconnected Measurement 23 50. 52. (a) (a) (c) 21. 1 m s v = ? v0 ? gt = v0 + gt v = v0 ? gt , d = 1 gt 2 2 29. 4 m s ? 202 m s 2 4. 53 s vi = h t + gt 2 (b) (b) 19. 6 m d = 1 gt 2 2 (c) 18. 1 m s, 19. 6 m 54. 56. 58. 60. 62. 64. (a) (a) (a) (a) (b) (b) (b) (b) 44. 1 m 198 m 14. m s v = h t ? gt 2 Experience Resolutions Section ce Agitation Diagrams. Yes. The reposeriction succor needed to exhaustive the 1 mile boundlessness in the ceeveryotted opportunity is amin = 0. 032 m s 2 , considerably hither than what she is cappotent of conceding. (a) (c) y1 = h ? v0 t ? 1 gt 2 , y2 = h + v0 t ? 1 gt 2 2 2 2 v1 f = v2 f = ? v0 + 2 gh (d) 66. (b) t 2 ? t1 = 2 v0 g y2 ? y1 = 2 v0 t as covet as twain globes are peaceful in the principle. 68. 70. 3. 10 m s (a) (c) 3. 00 s (b) v0 ,2 = ? 15. 2 m s v1 = ? 31. 4 m s, v2 = ? 34. 8 m s 2. 2 s simply if succor = 0 (b) (b) ? 21 m s Yes, ce ceentire judicious velocities and succors. 72. 74. (a) (a)
PROBLEM SOLUTIONS 2. 1 We affect that you are closely 2 m tentire and that the strength sudden-thought rustications at unvarying hurry. The late opportunity is then ? t = 2. 2 (a) 2m ? x = = 2 ? 10 ? 2 s = 0. 02 s v 100 m s At trustworthy hurry, c = 3 ? 108 m s, the boundlessness vain rustications in 0. 1 s is ? x = c ( ? t ) = ( 3 ? 108 m s ) ( 0. 1 s ) ? 1 mi ? ? 1 km ? 4 = ( 3 ? 10 7 m ) ? ? = 2 ? 10 mi ?? 3 ? 1. 609 km ? ? 10 m ? (b) Comparing the development of bisect-among-incompact (a) to the transection of the Earth, DE, we ? nd 3. 0 ? 10 7 m ? x ? x = = ? 2. 4 DE 2 RE 2 ( 6. 38 ? 10 6 m ) ( with RE = Earth’s radius ) http://helpyoustudy. info 24 Chapter 2 2. 3
Distances rusticationed betwixt pairs of cities are ? x1 = v1 ( ? t1 ) = (80. 0 km h ) ( 0. 500 h ) = 40. 0 km ? x2 = v2 ( ? t 2 ) = (100 km h ) ( 0. 200 h ) = 20. 0 km ? x3 = v3 ( ? t3 ) = ( 40. 0 km h ) ( 0. 750 h ) = 30. 0 km Thus, the incorpoadmonish boundlessness rusticationed is ? x = ( 40. 0 + 20. 0 + 30. 0 ) km = 90. 0 km, and the late opportunity is ? t = 0. 500 h + 0. 200 h + 0. 750 h + 0. 250 h = 1. 70 h. (a) (b) v= ? x 90. 0 km = = 52. 9 km h ? t 1. 70 h ?x = 90. 0 km (experience aloft) v= v= ? x 2. 000 ? 10 2 m = = 10. 04 m s ? t 19. 92 s 2. 4 (a) (b) 2. 5 (a) ?x 1. 000 mi ? 1. 609 km ? ? 10 3 m ? = ? ?? ? = 7. 042 m s ? t 228. 5 s ? 1 mi ? 1 km ? Boat A exacts 1. 0 h to morose the lake and 1. 0 h to recompense, incorpoadmonish opportunity 2. 0 h. Boat B exacts 2. 0 h to morose the lake at which opportunity the career is balance. Boat A wins, nature 60 km acommander of B when the career objects. Medium quickness is the intrap misinterpretation of the boat ceeveryotd by the incorpoadmonish late opportunity. The attractive boat is tail where it referpotent attributpotent attributpotent attributpotent attributpotent attributpotent attributpotent attributpotent attributableabilityted, its misinterpretation thus nature naught, resigning an medium quickness of naught . (b) 2. 6 The medium quickness balance any opportunity interim is ? x x f ? xi = ? t t f ? ti ? x 10. 0 m ? 0 v= = = 5. 00 m s ? t 2. 00 s ? 0 v= (a) (b) (c) (d) (e) v= v= v= v= ? x 5. 00 m ? 0 = = 1. 25 m s ? 4. 00 s ? 0 ? x 5. 00 m ? 10. 0 m = = ? 2. 50 m s ? t 4. 00 s ? 2. 00 s ? x ? 5. 00 m ? 5. 00 m = = ? 3. 33 m s ? t 7. 00 s ? 4. 00 s 0? 0 ? x x2 ? x1 = = = 0 ? t t 2 ? t1 8. 00 s ? 0 2. 7 (a) (b) 1h ? Misinterpretation = ? x = (85. 0 km h ) ( 35. 0 min ) ? ? ? + 130 km = 180 km ? 60. 0 min ? 1h ? The incorpoadmonish late opportunity is ? t = ( 35. 0 min + 15. 0 min ) ? ? ? + 2. 00 h = 2. 83 h ? 60. 0 min ? so, v= ? x 180 km = = 63. 6 km h ? t 2. 84 h http://helpyoustudy. info Agitation in Undisconnected Measurement 25 2. 8 The medium quickness balance any opportunity interim is ? x x f ? xi = ? t t f ? ti ? x 4. 0 m ? 0 v= = = + 4. 0 m s ? t 1. 0 s ? 0 ? ? 2 . 0 m ? 0 v= = = ? 0. 50 m s ? t 4. 0 s ? 0 v= (a) (b) (c) (d) v= v= ? x 0 ? 4. 0 m = = ? 1. 0 m s ? t 5. 0 s ? 1. 0 s ? x 0? 0 = = 0 ? t 5. 0 s ? 0 2. 9 The roll referpotent attributpotent attributpotent attributpotent attributpotent attributpotent attributpotent attributpotent attributableabilityts from repose ( v0 = 0 ) and maintains a trustworthy succor of a = +1. 3 m s 2 . Thus, we ? nd the boundlessness it achieve rustication precedently reaching the exactd siegeunpremeditated hurry ( v = 75 m s ) , from 2 v 2 = v0 + 2a ( ? x ) , as ? x = 2 v 2 ? v0 ( 75 m s ) ? 0 = = 2. 2 ? 10 3 m = 2. 2 km 2 2a 2 (1. 3 m s ) 2 Gundisconnected this boundlessness is hither than the diffusiveness of the runway, the roll sieges unpremeditated safely. 2. 10 (a) The opportunity ce a car to mould the err is t = cars to omplete the selfselfidentical 10 mile err is ? t = t1 ? t 2 = (b) ? x ? x ? 10 mi 10 mi ? ? 60 min ? ? =? ? ? = 2. 3 min ?? v1 v2 ? 55 mi h 70 mi h ? ? 1 h ? ?x . Thus, the dissentence in the opportunitys ce the span v When the faster car has a 15. 0 min transfer, it is acommander by a boundlessness correspondent to that rusticationed by the inactiveer car in a opportunity of 15. 0 min. This boundlessness is absorbed by ? x1 = v1 ( ? t ) = ( 55 mi h ) (15 min ). The faster car pulls acommander of the inactiveer car at a admonish of vrelative = 70 mi h ? 55 mi h = 15 mi h Thus, the opportunity exactd ce it to achieve boundlessness ? x1 acommander is ? t = ? x1 = vrelative ( 55 mi h ) (15 min ) 15. 0 mi h = 55 min
Finally, the boundlessness the faster car has rusticationed during this opportunity is ? x2 = v2 ( ? t ) = 2. 11 (a) ( 70 mi h ) ( 55 min ) ? ? 1h ? ? = 64 mi ? 60 min ? From v 2 = vi2 + 2a ( ? x ) , with vi = 0 , v f = 72 km h , and ? x = 45 m, the succor of the f cheetah is buildation to be ?? km ? ? 10 3 m ? ? 1 h ?? ?? 72 ?? ? 0 ?? ?? h ? ? 1 km ? ? 3 600 s ?? v 2 ? vi2 ?? f a= = = 4. 4 m s 2 2 ( ? x ) 2 ( 45 m ) abided on contiguous page 2 http://helpyoustudy. info 26 Chapter 2 (b) The cheetah’s misinterpretation 3. 5 s following referpotent attributpotent attributpotent attributpotent attributpotent attributpotent attributpotent attributpotent attributableabilityting from repose is 1 1 2 ? x = vi t + at 2 = 0 + ( 4. 4 m s 2 ) ( 3. 5 s ) = 27 m 2 2 2. 12 (a) (b) (c) (d) 1 = v2 = ( ? x )1 + L = = + L t1 ( ? t )1 t1 ( ? x )2 ? L = = ? L t2 ( ? t )2 t 2 ( ? x ) incorpoadmonish ( ? x )1 + ( ? x )2 + L ? L 0 = = = 0 = t1 + t 2 t1 + t 2 t1 + t 2 ( ? t ) incorpoadmonish +L + ? L incorpoadmonish boundlessness rusticationed ( ? x )1 + ( ? x )2 2L = = = ( ave. hurry )err = t1 + t 2 t1 + t 2 t1 + t 2 ( ? t ) incorpoadmonish vincorpoadmonish = The incorpoadmonish opportunity ce the err is t incorpoadmonish = t1 + 22 . 0 min = t1 + 0. 367 h , where t1 is the opportunity late rusticationing at v1 = 89. 5 km h. Thus, the boundlessness rusticationed is ? x = v1 t1 = vt incorporate, which communicates 2. 13 (a) (89. 5 km h ) t1 = ( 77. 8 km h ) ( t1 + 0. 367 h ) = ( 77. 8 km h ) t1 + 28. 5 km or, (89. 5 km h ? 77. km h ) t1 = 28. 5 km From which, t1 = 2 . 44 h ce a incorpoadmonish opportunity of t incorpoadmonish = t1 + 0. 367 h = 2. 81 h (b) The boundlessness rusticationed during the err is ? x = v1 t1 = vt incorporate, giving ? x = v tincorpoadmonish = ( 77. 8 km h ) ( 2. 81 h ) = 219 km 2. 14 (a) At the object of the career, the tortoise has been affecting ce opportunity t and the uncommon ce a opportunity t ? 2 . 0 min = t ? 120 s. The hurry of the tortoise is vt = 0. 100 m s, and the hurry of the uncommon is vh = 20 vt = 2 . 0 m s. The tortoise rustications boundlessness xt, which is 0. 20 m abundantr than the boundlessness xh rusticationed by the uncommon. Hereafter, xt = xh + 0. 20 m which beseems or vt t = vh ( t ? 120 s ) + 0. 0 m ( 0. 100 m s ) t = ( 2 . 0 m s ) ( t ? 120 s ) + 0. 20 m t = 1. 3 ? 10 2 s This communicates the opportunity of the career as (b) 2. 15 xt = vt t = ( 0. 100 m s ) (1. 3 ? 10 2 s ) = 13 m The acme ceeveryowed opportunity to exhaustive the err is t incorpoadmonish = incorpoadmonish boundlessness 1600 m ? 1 km h ? = ? ? = 23. 0 s exactd medium hurry 250 km h ? 0. 278 m s ? The opportunity late in the ? rst half of the err is t1 = half boundlessness 800 m ? 1 km h ? = ? ? = 12 . 5 s v1 230 km h ? 0. 278 m s ? abided on contiguous page http://helpyoustudy. info Agitation in Undisconnected Measurement 27 Thus, the acme opportunity that can be late on the succor half of the err is t 2 = t incorpoadmonish ? 1 = 23. 0 s ? 12 . 5 s = 10. 5 s and the exactd medium hurry on the succor half is v2 = 2. 16 (a) ? 1 km h ? half boundlessness 800 m = = 76. 2 m s ? ? = 274 km h t2 10. 5 s ? 0. 278 m s ? In adorderly ce the luxuriance athlete to be potent to lay-hold-on the director, his hurry (v1) must be superior than that of the transfering athlete (v2), and the boundlessness betwixt the transfering athlete and the ? nish succession must be grmunch abundance to communicate the luxuriance athlete suf? cient opportunity to mould up the de? cient boundlessness, d. During a opportunity t the transfering athlete achieve rustication a boundlessness d2 = v2 t and the luxuriance athlete achieve rustication a boundlessness d1 = v1t .
Simply when d1 = d2 + d (where d is the judicious boundlessness the luxuriance athlete was rearwards the director) achieve the luxuriance athlete keep caught the director. Requiring that this mode be satis? ed communicates the late opportunity exactd ce the succor athlete to balancesiege the ? rst: d1 = d2 + d giving or v1t = v2 t + d or t = d ( v1 ? v2 ) (b) v1t ? v2 t = d (c) In adorderly ce the luxuriance athlete to be potent to at decisive fasten ce ? rst assign, the judicious boundlessness D betwixt the director and the ? nish succession must be superior than or correspondent to the boundlessness the director can rustication in the opportunity t fitted aloft (i. e. , the opportunity exactd to balancesiege the director).
That is, we must exact that D ? d2 = v2 t = v2 ? d ( v1 ? v2 ) ? ? ? or D? v2 d v1 ? v2 2. 17 The minuteaneous quickness at any opportunity is the arise of the x vs. t graph at that opportunity. We appraise this arise by using span purposes on a rectilinear bisect of the flexion, undisconnected purpose on each roll of the purpose of share. (a) (b) (c) (d) vt=1. 00 s = vt=3. 00 s = 10. 0 m ? 0 = 5. 00 m s 2 . 00 s ? 0 ( 5. 00 ? 10. 0 ) m = ? 2 . 50 m s ( 4. 00 ? 2 . 00 ) s ( 5. 00 ? 5. 00 ) m vt=4. 50 s = = 0 ( 5. 00 ? 4. 00 ) s 0 ? ( ? 5. 00 m ) vt=7. 50 s = = 5. 00 m s (8. 00 ? 7. 00 ) s http://helpyoustudy. info 28 Chapter 2 2. 18

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