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 1249: 37.28


a.$v=0.140c$. b. $v=0.417c$. c. $v=0.866c$.

Work Step by Step

The value of $\gamma$ is $\frac{1}{\sqrt{1-v^{2}/c^{2}}}$. a. Solve for v when $\gamma=\frac{1}{\sqrt{1-v^{2}/c^{2}}}=1.010$ $$v=c\sqrt{1-1/\gamma^2}=0.140c$$ b. Solve for v when $\gamma=\frac{1}{\sqrt{1-v^{2}/c^{2}}}=1.10$ $$v=c\sqrt{1-1/\gamma^2}=0.417c$$ c. Solve for v when $\gamma=\frac{1}{\sqrt{1-v^{2}/c^{2}}}=2.00$ $$v=c\sqrt{1-1/\gamma^2}=0.866c$$
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