Physics for Scientists and Engineers: A Strategic Approach with Modern Physics (4th Edition)

Published by Pearson
ISBN 10: 0133942651
ISBN 13: 978-0-13394-265-1

Chapter 10 - Interactions and Potential Energy - Exercises and Problems: 7

Answer

The skateboarder needs a speed of 7.7 m/s at the bottom.

Work Step by Step

The kinetic energy at the bottom of the quarter pipe should be equal to the potential energy at the top of the quarter pipe which is at the height $h = 3.0~m$. Therefore; $KE = PE$ $\frac{1}{2}mv^2 = mgh$ $v^2 = 2gh$ $v = \sqrt{2gh}$ $v = \sqrt{(2)(9.80~m/s^2)(3.0~m)}$ $v = 7.7~m/s$ The skateboarder needs a speed of 7.7 m/s at the bottom.
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