Fundamentals of Physics Extended (10th Edition)

Published by Wiley
ISBN 10: 1-11823-072-8
ISBN 13: 978-1-11823-072-5

Chapter 37 - Relativity - Problems - Page 1152: 94e

Answer

$t = \frac{0.167~D}{c}$

Work Step by Step

We can find the total distance $d$ as measured from the rest frame of the starship: $d = \frac{4D}{\gamma}$ $d = \frac{4D}{24}$ $d = 0.167~D$ We can find $\beta$: $\gamma = \frac{1}{\sqrt{1-\beta^2}}$ $\sqrt{1-\beta^2} = \frac{1}{\gamma}$ $1-\beta^2 = \frac{1}{\gamma^2}$ $\beta^2 = 1-\frac{1}{\gamma^2}$ $\beta = \sqrt{1-\frac{1}{\gamma^2}}$ $\beta = \sqrt{1-\frac{1}{24^2}}$ $\beta = 0.99913$ We can find the travel time as measured from the rest frame of the starship: $t = \frac{0.167 D}{0.99913~c}$ $t = \frac{0.167~D}{c}$
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