University Physics with Modern Physics (14th Edition)

Published by Pearson
ISBN 10: 0321973615
ISBN 13: 978-0-32197-361-0

Chapter 37 - Relativity - Problems - Exercises - Page 1249: 37.21



Work Step by Step

Use the Lorentz Transformation formula for relative velocity. $v_x=(v'_x+u)/(1+(v'_x u)/c^2 )$ Given in the question that relative velocity is equal to 0.890c and that u and v’x are equal (so let v’x also equal u) $0.890c=2u/(1+(u)(u))$ Rearrange into a linear quadratic in terms of u 0.890c(u2) -2u + 0.890c = 0 use quadratic formula $(-b±√(b^2-4ac))/2a$ u = 0.611c or u = 1.64c however we know that no particle can move at a speed greater than c so u must be equal to 0.611c therefore u = 0.611c
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