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HW8_Solutions

# HW8_Solutions - hiarker(srh959 homework 08 Turner(58220...

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hiarker (srh959) – homework 08 – Turner – (58220) 1 This print-out should have 13 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 car is parked on a cliff overlooking the ocean on an incline that makes an angle of 31 . 2 below the horizontal. The negligent driver leaves the car in neutral, and the emergency brakes are defective. The car rolls from rest down the incline with a constant acceleration of 5 . 85 m / s 2 and travels 68 m to the edge of the cliff. The cliff is 31 . 3 m above the ocean. The acceleration of gravity is 9 . 8 m / s 2 . Find the car’s position relative to the base of the cliff when the car lands in the ocean. Correct answer: 34 . 8252 m. Explanation: Given : a = 5 . 85 m / s 2 , l = 68 m , h = 31 . 3 m , and θ = 31 . 2 . The speed of the car when it reaches the edge of the cliff is given by v 2 = v 2 i + 2 a l = 2 a l since v i = 0 m / s, so v = 2 a ℓ = radicalBig 2 (5 . 85 m / s 2 ) (68 m) = 28 . 2064 m / s . Now, consider the projectile phase of the car’s motion. The initial vertical velocity is v iy = v sin θ = (28 . 2064 m / s) sin(31 . 2 ) = 14 . 6117 m / s . and the vertical velocity with which the car strikes the water is v 2 y = v 2 iy + 2 g h = v 2 sin 2 θ + 2 g h = (28 . 2064 m / s) 2 sin 2 31 . 2 + 2 ( 9 . 8 m / s 2 ) (31 . 3 m) = 826 . 981 m 2 / s 2 , so that v y = radicalBig 826 . 981 m 2 / s 2 = 28 . 7573 m / s . To find the time of flight, v y = v iy + g Δ t Δ t = v y - v iy g The initial horizontal velocity is v ix = v cos θ and the horizontal motion of the car during this time is x = v ix Δ t = ( v cos θ ) v y - v iy g = (28 . 2064 m / s) cos 31 . 2 × (28 . 7573 m / s) - (14 . 6117 m / s) (9 . 8 m / s 2 ) = 34 . 8252 m . 002 (part 2 of 2) 10.0 points Find the length of time the car is in the air. Correct answer: 1 . 44343 s. Explanation: Using the vertical motion, v y = v iy + g t t = v y - v iy g = (28 . 7573 m / s) - (14 . 6117 m / s) (9 . 8 m / s 2 ) = 1 . 44343 s . 003 10.0 points A soccer player kicks a rock horizontally off a 39 . 8 m high cliff into a pool of water.

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hiarker (srh959) – homework 08 – Turner – (58220) 2 The acceleration of gravity is 9 . 8 m / s 2 .
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