Physics: Principles with Applications (7th Edition)

Published by Pearson
ISBN 10: 0-32162-592-7
ISBN 13: 978-0-32162-592-2

Chapter 26 - The Special Theory of Relativity - Problems - Page 769: 52

Answer

0.78 c

Work Step by Step

Let the positive direction be the direction of both rockets. Let rocket A’s reference frame be S and the Earth’s reference frame be S’. The velocity of the Earth relative to rocket A is v = -0.65c. The velocity of rocket B relative to the Earth is u’=+0.95c. Use the relativistic velocity addition formula, equation 26–10, to find the velocity of rocket B as measured by rocket A. $$u=\frac{v+u’}{1+\frac{vu’}{c^2}}$$ $$u=\frac{-0.65c+0.95c}{1+(-0.65)(0.95)}=0.78c$$
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