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17 - roofner(bar784 Homework 17 Weathers(17104 This...

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roofner (bar784) – Homework 17 – Weathers – (17104) 1 This print-out should have 10 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) Find the time it takes an object to hit the ground when it is dropped from a height of 66 using the model h = - 16 t 2 + s, where s is the initial height, and t is in sec- onds. Correct answer: 2 . 03101 sec. Explanation: h = - 16 t 2 + 66 The ball hits the ground at h = 0, so 0 = - 16 t 2 + 66 16 t 2 = + 66 16 t 2 16 = 66 16 t 2 = 4 . 125 t 2 = ± 4 . 125 t ≈ ± 2 . 03101 Time must be positive, so t 2 . 03101 sec . 002 (part 2 of 2) 10.0 points b) Find the time it takes an object to hit the ground when it is dropped from a height of 132 ft. Correct answer: 2 . 87228. Explanation: h = - 16 t 2 + 132 The ball hits the ground at h = 0. Thus the time of fall can be found from 0 = - 16 t 2 + 132 16 t 2 = + 132 16 t 2 16 = 132 16 t 2 = 8 . 25 t 2 = ± 8 . 25 t ≈ ± 2 . 87228 t cannot be negative, so t 2 . 87228 . Note that doubling the distance does not dou- ble the time. 003 (part 1 of 2) 10.0 points Given: G = 6 . 67259 × 10 - 11 N m 2 / kg 2 Two hypothetical planets of masses 3 . 2 × 10 23 kg and 6 . 1 × 10 23 kg and radii 3 . 9 × 10 6 m and 7 . 8 × 10 6 m, respectively, are at rest when they are an infinite distance apart. Because of their gravitational attraction, they head toward each other on a collision course. When their center-to-center separation is 7 . 4 × 10 8 m, find their relative velocity. Correct answer: 408 . 967 m / s. Explanation: At infinite separation the potential energy U is zero, and at rest the kinetic energy K is zero. Since energy is conserved we have 0 = 1 2 m 1 v 2 1 + 1 2 m 2 v 2 2 - G m 1 m 2 d . The initial momentum is zero and momentum is conserved, so 0 = m 1 v 1 - m 2 v 2 . Combine these two equations to find v 1 = m 2 radicalBigg 2 G d ( m 1 + m 2 ) = 6 . 1 × 10 23 kg × radicalBigg 2 (6 . 67259 × 10 - 11 N m 2 / kg 2 ) (7 . 4 × 10 8 m) (9 . 3 × 10 23 kg) = 268 . 247 m / s v 2 = m 1 radicalBigg 2 G d ( m 1 + m 2 ) = 3 . 2 × 10 23 kg × radicalBigg 2 (6 . 67259 × 10 - 11 N m 2 / kg 2 ) (7 . 4 × 10 8 m) (9 . 3 × 10 23 kg) = 140 . 72 m / s .
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