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Homework 17 Solutions

# Homework 17 Solutions - lim(kl9356 Homework 17...

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lim (kl9356) – 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 67 using the model h = - 16 t 2 + s, where s is the initial height, and t is in sec- onds. Correct answer: 2 . 04634 sec. Explanation: h = - 16 t 2 + 67 The ball hits the ground at h = 0, so 0 = - 16 t 2 + 67 16 t 2 = + 67 16 t 2 16 = 67 16 t 2 = 4 . 1875 t 2 = ± 4 . 1875 t ≈ ± 2 . 04634 Time must be positive, so t 2 . 04634 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 134 ft. Correct answer: 2 . 89396. Explanation: h = - 16 t 2 + 134 The ball hits the ground at h = 0. Thus the time of fall can be found from 0 = - 16 t 2 + 134 16 t 2 = + 134 16 t 2 16 = 134 16 t 2 = 8 . 375 t 2 = ± 8 . 375 t ≈ ± 2 . 89396 t cannot be negative, so t 2 . 89396 . 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 4 × 10 23 kg and 7 . 7 × 10 23 kg and radii 4 . 8 × 10 6 m and 6 . 1 × 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 5 . 5 × 10 8 m, find their relative velocity. Correct answer: 532 . 822 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 ) = 7 . 7 × 10 23 kg × radicalBigg 2 (6 . 67259 × 10 - 11 N m 2 / kg 2 ) (5 . 5 × 10 8 m) (1 . 17 × 10 24 kg) = 350 . 661 m / s v 2 = m 1 radicalBigg 2 G d ( m 1 + m 2 ) = 4 × 10 23 kg × radicalBigg 2 (6 . 67259 × 10 - 11 N m 2 / kg 2 ) (5 . 5 × 10 8 m) (1 . 17 × 10 24 kg) = 182 . 161 m / s .

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Homework 17 Solutions - lim(kl9356 Homework 17...

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