Physics for Scientists and Engineers: A Strategic Approach with Modern Physics (3rd Edition)

Published by Pearson
ISBN 10: 0321740904
ISBN 13: 978-0-32174-090-8

Chapter 10 - Energy - Exercises and Problems - Page 271: 3

Answer

$112\;\rm km/h$

Work Step by Step

We know that the two vehicles are having the same kinetic energy. $$K_{car}=K_{truck}$$ Thus, $$\frac{1}{2}m_{car}v_{car}^2=\frac{1}{2}m_{truck}v_{truck}^2$$ $$ m_{car}v_{car}^2= m_{truck}v_{truck}^2$$ Solving for the $v_{car}$; $$ v_{car}^2= \dfrac{m_{truck}v_{truck}^2}{m_{car}}$$ $$ v_{car} =\sqrt{ \dfrac{m_{truck}v_{truck}^2}{m_{car}}}$$ Plugging the known; $$ v_{car} =\sqrt{ \dfrac{20,000\times 25^2}{1000}}\approx \color{red}{\bf 112}\;\rm km/h$$
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