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homework 2 - narainswamy(ann452 HW2 Mackie(20211 This...

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narainswamy (ann452) – HW2 – Mackie – (20211) 1 This print-out should have 17 questions. Multiple-choice questions may continue on the next column or page – find all choices before answering. 001 (part 1 of 2) 10.0 points A speeder passes a parked police car at a constant speed of 34 . 5 m / s. At that instant, the police car starts from rest with a uniform acceleration of 2 . 08 m / s 2 . How much time passes before the speeder is overtaken by the police car? Correct answer: 33 . 1731 s. Explanation: Let : v = 34 . 5 m / s and a = 2 . 08 m / s 2 . x = v i t + 1 2 at 2 Since the speeder has no acceleration, his position is given by x s = vt. The policeman starts from rest, so x p = 1 2 at 2 . The cop overtakes the speeder when x s = x p vt = 1 2 at 2 0 = at 2 - 2 vt 0 = ( at - 2 v ) t t = 2 v a = 2 (34 . 5 m / s) 2 . 08 m / s 2 = 33 . 1731 s . 002 (part 2 of 2) 10.0 points How far does the speeder travel before being overtaken by the police car? Correct answer: 1144 . 47 m. Explanation: The distance may be obtained with either d = vt = (34 . 5 m / s) (33 . 1731 s) = 1144 . 47 m or d = 1 2 at 2 = 1 2 ( 2 . 08 m / s 2 ) (33 . 1731 s) 2 = 1144 . 47 m . 003 (part 1 of 2) 10.0 points A stone falls from rest from the top of a cliff. A second stone is thrown downward from the same height 3 s later with an initial speed of 58 . 8 m / s. They hit the ground at the same time. The acceleration of gravity is 9 . 8 m / s 2 . How long does it take the first stone to hit the ground? Correct answer: 4 . 5 s. Explanation: For stone 1: y 1 = 1 2 g t 2 1 For stone 2: y 2 = v 0 t 2 + g t 2 2 2 Stone 2 is thrown Δ t seconds after stone 1 and they hit the ground at the same time, so t 1 = t 2 + Δ t. Since the height of the cliff is the same for both of the stones, y 1 = y 2 g t 2 1 2 = v 0 ( t 1 - Δ t ) + g 2 ( t 1 - Δ t ) 2 ( v 0 - g Δ t ) t 1 = v 0 Δ t - g 2 Δ t 2 t 1 = v 0 Δ t - g 2 Δ t 2 v 0 - g Δ t = (58 . 8 m / s) (3 s) (58 . 8 m / s) - (9 . 8 m / s 2 ) (3 s) - (9 . 8 m / s 2 ) 2 (3 s) 2 (58 . 8 m / s) - (9 . 8 m / s 2 ) (3 s) = 4 . 5 s .
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narainswamy (ann452) – HW2 – Mackie – (20211) 2 004 (part 2 of 2) 10.0 points How high is the cliff?
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