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 768: 48

Answer

a. 0.882c. b. -0.882c. As expected, the relative velocity in part a is the negative of the relative velocity in part b.

Work Step by Step

a. Reference frame S is the second spaceship and reference frame is the Earth. Let the direction of the first spaceship be the positive direction. We see that v = 0.60c because this is the velocity of Earth relative to the second spaceship. The velocity of the first spaceship relative to the Earth is given as u’=0.60c. Use equation 26–10 to solve for the velocity of the first spaceship relative to the second spaceship. $$u=\frac{v+u’}{(1+\frac{vu’}{c^2})}=\frac{0.60c+0.60c}{1+(0.60)(0.60)}=0.882c$$ b. Reference frame S is the first spaceship and reference frame is the Earth. Let the direction of the first spaceship be the positive direction. We see that v = -0.60c because this is the velocity of Earth relative to the first spaceship. The velocity of the second spaceship relative to the Earth is given as u’=-0.60c. Use equation 26–10 to solve for the velocity of the second spaceship relative to the first spaceship. $$u=\frac{v+u’}{(1+\frac{vu’}{c^2})}=\frac{-0.60c-0.60c}{1+(-0.60)(-0.60)}=-0.882c$$ As expected, the relative velocity in part a is the negative of the relative velocity in part b.
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