Special Relativity - Relativistic Addition of Velocities

An atom moving at speed 0.3c emits an electron along the same direction with speed 0.6c in the internal rest frame of the atom. The speed of the electron in the lab frame equal to

A. 0.25c
B. 0.51c
C. 0.66c
D. 0.76c
E. 0.90c

(GR9677 #37)

Solution:

Relativistic Addition of Velocities:

v = speed of the moving observer
u' = speed of object in the moving observer
u = speed of object in the moving observer relative to the rest observer

Given:
v = speed of atom = 0.3c
u' = speed of electron in the rest frame of the atom = 0.6c

u = speed of electron in the lab frame
= (0.6c + 0.3c) / [1 + (0.6)(0.3)]
= 0.9c /1.18 
= 90/118 
= 0.762c