Physics for Scientists and Engineers: A Strategic Approach with Modern Physics (4th Edition)

Published by Pearson
ISBN 10: 0133942651
ISBN 13: 978-0-13394-265-1

Chapter 36 - Relativity - Exercises and Problems - Page 1061: 54

Answer

The speed of one rocket relative to the other is $~~0.96~c~~$

Work Step by Step

Let $u'$ be Rocket A's velocity relative to the earth reference frame. Let $v$ be the earth's velocity relative to Rocket B. Let $u$ be Rocket A's velocity relative to Rocket B. We can find $u$: $u = \frac{u'+v}{1+\frac{u'v}{c^2}}$ $u = \frac{0.75c+0.75c}{1+\frac{(0.75c)(0.75c)}{c^2}}$ $u = \frac{1.5c}{1+0.5625}$ $u = 0.96~c$ The speed of one rocket relative to the other is $~~0.96~c~~$
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