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solution10_pdf - arellano(aa39398 Homework 6 Weathers(17101...

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arellano (aa39398) – Homework 6 – Weathers – (17101) 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 car travels due east with a horizontal speed of 59 . 8 km / h. Rain is falling vertically with respect to Earth. The traces of the rain on the side windows of the car make an angle of 64 with the vertical. Find the magnitude of the velocity of the rain with respect to the car. Correct answer: 66 . 5336 km / h. Explanation: Taking down and west be positive, let v ce = velocity of car relative to Earth, v rc = velocity of rain relative to car, and v re = velocity of rain relative to Earth. Given : v ce = 59 . 8 km / h and θ = 64 . The car is moving out from under the rain, so the rain streaks are westward toward the rear bumper. v rc 59 . 8 km / h v re 64 Note: Figure is not drawn to scale sin θ = v ce v rc v rc = v ce sin θ = 59 . 8 km / h sin 64 = 66 . 5336 km / h at 64 west of vertical. 002 (part 2 of 2) 10.0 points Find the magnitude of the rain’s velocity with respect to Earth. Correct answer: 29 . 1664 km / h. Explanation: cos θ = v re v rc v re = v rc cos θ = (66 . 5336 km / h) cos 64 = 29 . 1664 km / h . 003 10.0 points A boat moves through the water of a river at 6 . 92 m / s relative to the water, regardless of the boat’s direction. If the current is flowing at 3 . 59 m / s, how long does it take the boat to complete a trip consisting of a 174 m displacement down- stream followed by a 122 m displacement up- stream? Correct answer: 53 . 1923 s. Explanation: Let v b be the velocity of the boat relative to the water, and v w the velocity of water relative to the shore. Take downstream as the positive direction. For the downstream trip, the current is speeding him up, so the velocity of the boat relative to the shore is v d = v b + v w and the time is t d = x d v d = x d v b + v w For the upstream trip, the current is slowing him down, so the velocity of the boat relative to the shore is v u = v b - v w and the time is t u = x u v u = x u v b - v w
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