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: 49

Answer

a. 0.96c. b. 0.36c.

Work Step by Step

a. Let the direction of the first spaceship be the positive direction. Reference frame S is the Earth and reference frame is the first spaceship. We see that v = 0.65c. The speed of the second spaceship relative to the first spaceship is given as u’=0.82c. Use equation 26–10 to solve for the speed of the second spaceship relative to the Earth. $$u=\frac{v+u’}{(1+\frac{vu’}{c^2})}=\frac{0.65c+0.82c}{1+(0.65)(0.82)}=0.96c$$ b. Now, $u’=-0.82c$. $$u=\frac{v+u’}{(1+\frac{vu’}{c^2})}=\frac{0.65c-0.82c}{1+(0.65)(-0.82)}=-0.36c$$ The problems asks for "speed", so the answer is 0.36c.
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