University Physics with Modern Physics (14th Edition)

Published by Pearson
ISBN 10: 0321973615
ISBN 13: 978-0-32197-361-0

Chapter 37 - Relativity - Problems - Exercises - Page 1253: 37.74


Choice B.

Work Step by Step

The value of $\gamma$ is $\frac{1}{\sqrt{1-v^{2}/c^{2}}}$. The relativistic kinetic energy is $(\gamma-1)mc^2$. Here, we are told that $(\gamma-1)mc^2=mc^2$, so we know that $\gamma= 2$. Solve for v when $\gamma=\frac{1}{\sqrt{1-v^{2}/c^{2}}}=2.00$ $$v=c\sqrt{1-1/\gamma^2}=0.866c$$ $$v=0.866(300m/s) = 260 m/s$$
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