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# oldhw 08 - alexander(jra2623 oldhomework 08 Turner(92510...

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alexander (jra2623) – oldhomework 08 – Turner – (92510) 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 10.0 points A soccer player kicks a rock horizontally off a 39 . 4 m high cliff into a pool of water. The acceleration of gravity is 9 . 8 m / s 2 . If the player hears the sound of the splash 3 . 79 s later, what was the initial speed given to the rock? Assume the speed of sound in air to be 343 m / s. Correct answer: 114 . 602 m / s. Explanation: Given : y i = - 39 . 4 m , g = 9 . 8 m / s 2 , and t splash = 3 . 79 s . The rock follows a parabolic path and the sound comes back in a straight line. Δ x Δ y Δ x Δ y d The time of flight can be obtained from the vertical motion: Δ y = v iy t - 1 2 g t 2 = - 1 2 g t 2 since v iy = 0, so t flight = radicalBigg - 2 Δ y g = radicalBigg - 2 ( - 39 . 4 m) 9 . 8 m / s 2 = 2 . 83563 s . Since the player hears the sound of the splash 3 . 79 s after the kick, the time required for the sound to travel straight back to the player is t sound = t splash - t flight = 3 . 79 s - 2 . 83563 s = 0 . 954367 s . and the straight line distance from the point the rock hits the water to the player is d = v sound t sound = (343 m / s) (0 . 954367 s) = 327 . 348 m . Since d 2 = (Δ x ) 2 + (Δ y ) 2 , the horizontal distance the rock travels is Δ x = radicalBig d 2 - y ) 2 = v ix t flight . Thus v ix = radicalbig d 2 - y ) 2 t flight = radicalbig (327 . 348 m) 2 - (39 . 4 m) 2 2 . 83563 s = 114 . 602 m / s . 002 (part 1 of 2) 10.0 points The pilot of an aircraft wishes to fly due west in a 82 km / h wind blowing toward the south.

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