College Physics (4th Edition)

Published by McGraw-Hill Education
ISBN 10: 0073512141
ISBN 13: 978-0-07351-214-3

Chapter 26 - Problems - Page 1013: 73


$v = 0.66~c$

Work Step by Step

We can find $\gamma$: $\Delta t = \gamma~\Delta t_0$ $\gamma = \frac{\Delta t}{\Delta t_0}$ $\gamma = \frac{4~days}{3~days}$ $\gamma = 1.33$ We can find the speed relative to the space station: $\gamma = \frac{1}{\sqrt{1-\frac{v^2}{c^2}}}$ $1-\frac{v^2}{c^2} = \frac{1}{\gamma^2}$ $\frac{v^2}{c^2} = 1-\frac{1}{\gamma^2}$ $v^2 = [1-\frac{1}{\gamma^2}~]~c^2$ $v = \sqrt{1-\frac{1}{\gamma^2}}~\times c$ $v = \sqrt{1-\frac{1}{1.33^2}}~\times c$ $v = 0.66~c$
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