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 - General Problems - Page 770: 71

Answer

0.981c

Work Step by Step

Let the positive direction be the direction of particle 2, and find the velocity of particle 2 as measured by particle 1. The answer will be positive. Let the first particle’s reference frame be S and the lab’s reference frame be S’. The velocity of the lab relative to the first particle is v = +0.82c. The velocity of the second particle relative to the spacecraft is u’=+0.82c. Use the relativistic velocity addition formula, equation 26–10, to find the velocity of the second particle as measured by the first particle. $$u=\frac{v+u’}{1+\frac{vu’}{c^2}}$$ $$u=\frac{0.82c+0.82c}{1+(0.82)(0.82)}=0.981c$$
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