Frame S' moves in the positive x direction at 0.6c with respect to frame S.A particle moves in the positive x direction at 0.4c as measured by an observer in S'.The speed of the particle as measured by an observer in S is:
A)c/5
B)5c/19
C)8c/25
D)25c/31
E)c

Question

Quizplus · Accepted Answer

We can use the relativistic velocity addition formula to find the speed of the particle as measured by an observer in S:

v = (v' + u) / (1 + v'u/c^2)

where v' is the speed of the particle in S' (0.4c) and u is the speed of S' relative to S (0.6c).

Plugging in the values, we get:

v = (0.4c + 0.6c) / (1 + 0.4c*0.6c/c^2) = 0.8c / (1 + 0.24) = 0.8c / 1.24 = 25c/31

Therefore, the answer is D.

Frame S' Moves in the Positive X Direction at 0