Fundamentals of Physics Extended (10th Edition)

Published by Wiley
ISBN 10: 1-11823-072-8
ISBN 13: 978-1-11823-072-5

Chapter 2 - Motion Along a Straight Line - Problems: 53

Answer

3.96 m/s

Work Step by Step

We are told that the boat is 12m from the point of impact when the key is released. In order to find the velocity, we need to find the time that it took the boat to travel these 12m and then divide the displacement by the time. We know that the time it took the boat to travel this distance is the same as the time it took the key to fall. Therefore, we have that the key has an initial position of 45m and since it was dropped (it fell), it has an initial velocity, v0 of 0m/s. The acceleration is that of gravity $ a = -9.81 m/s^2 $. We use the equation $ x = x0 +v0*t +(1/2)at^2 $ and solve for when x =0 (the apple hits the ground/boat) $ 0 = 45m + 0*t +(1/2)(-9.81m/s^2)t^2 $ $-45m = (-4.89m/s^2)t^2 $ so then t = 3.03s Therefore the boat travels 12m in 3.03s so the velocity is 12m/3.03s = 3.96m/s
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