page 129 Question Relative Motion

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6 page 130 Question - 30 a) What is the ratio of v B to v R? b) If the boat heads toward point G, where will it reach on the opposite riverbank? 6

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9 page 131 Question = v y.8 v y = 12 m / s 15 2 = v x 2 v x = 9 m / s From A to B; the horizontal displacement is zero. v river = v x = 9 m / s 9

10 page 131 Question - 34 Choose east as "+ " direction. vk = +10 m / s vkl = +4 m / s vlm = -2 m / s vkl = vk- vl +4 = v L v L = +6 m / s vlm = vl- vm -2 = +6 - v M v M = +8 m / s 10

11 page 131 Question - 35 For boat B; v Bx = v B.cos53 o = 5.0,6 = 3 m / s v By = v B.sin53 o = 5.0,8 = 4 m / s t B = 16 4 = 4 s For boat A; t A = 16 4 = 4 s X B = (v r + v Bx ).t A X B = (2 + 3).4 X B = 20 m () X A = v r.t A X A = 2.4 X A = 8 m () The distance between them when they reach the opposite riverbank is 20-8 = 12 m 11

12 page 131 Question - 36 v CB = v C v B vcb = 18 m/s due east vc = 10 m/s They move in opposite directions. vb = 8 m/s Car is moving due east and bus due west. v MB = vm vb v CB = 7 m/s vm = 15 m/s They move in the same direction. vb = 8 m/s Bus and motor are moving due west. P a) The car moves in front of the motor. The information given in the question is not enough to know the statement is correct or not. P b) c) The bus and the car move toward each other. Bus and car are moving opposite directions. They move toward each other or move away from each other. W A d) e) The motor moves due east. Motor moves in the same direction as the bus which is due west. The bus moves due west. Bus moves due west. P The distance between motor and the bus decreases as the time passes. Bus and motor are moving opposite directions. The distance between them may decreases if they are moving toward each other. 12

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15 page 132 Question - 39 They are moving on the same lane, so they are moving in the same direction. Truck is moving due east and car moves due west with respect to the truck. This means that the speed of truck is greater. P c) The car is behind the truck and it is stationary. P a) The car is moving in front of the truck and it is slower than the truck. P d) The car is behind the truck and it is slower than the truck. P b) The car is in front of the truck and it is stationary. W e) The car is behind the truck and it is faster than the truck. 15

16 page 132 Question direction vman(wrt ground) = 8v v = +7v vgirl(wrt truck A) + 9v = +7v vgirl(wrt ground) = +7v vgirl(wrt truck A) = 2v Because she is stationary wrt man. 2v to the left. 16

17 page 133 Question - 41 v 1X = v river = v 2x = v 1y.3t v 1 = v 1y = 2x 3t = 2v 3 4v2 9 + v2 v 1 = 13 3.v For swimmer D; 3x = v.t 1 For swimmer E; x = v.t 2 t 2 = t t 1 = 3t t 1 t 2 = 3 2x = v 2.t v 2 = 2x t v 1 v 2 = 13 3.v 2v = 13 6 = 2v 17

18 page 133 Question - 42 A a) The speed of car B is greater than the speed of car A. v v 1 = vb vc v 1 = v B + v c 2 = v A vc v 2 = v A + v c P b) The speed of car B is smaller than the speed of car C. v 1 > v 2 v B + v c > v A + v c then v B > v A We cannot compare v c with the others. P c) The speed of car A is equal to the speed of car C. 18

19 page 133 Question - 43 Their vertical componets are the same. So, their times to reach the opposite riverbank are equal. X A = (16 + 4).t = 20t 20t = k v Bx = 15.0,6 = 9 m/s v By = 15.0,8 = 12 m/s v Ax = 20.0,8 = 16 m/s v Ay = 20.0,6 = 12 m/s X B = (9 4).t = 5t X B = k 4 The distance between them is d=k + k 4 = 5k 4 19

20 page 133 Question - 44 The velocity of X wrt ground is v boat+ v river + vx = 0 2v + v + vx = 0 X is stationary wrt Y. So, velocity of X must be zero wrt ground. vx = +v + direction 20