Question

A body initially moving at 0.500c with respect to a stationary observer disintegrates into two fragments that move in opposite directions relative to the centre of mass along the same line of motion as the original body. After disintegration, one fragment has a velocity of 0.600c in the backward direction in the centre of mass frame and the other has a velocity of 0.500c in the forward direction. What velocities will the observer measure for the two fragments?

Answer 1

Answer:0.846 c, 0

Explanation:

Giving

Body is initially moving with 0.5 c

The velocity of the fragment which is moving with velocity of 0.6  c is appears to be move with velocity of

$v_0=\frac{u+v}{1+\frac{uv}{c^2}}$

$v_0=\frac{0.5c+0.6c}{1+\frac{0.5c\cdot 0.6c}{c^2}}$

$v_0=\frac{1.1c}{1.3}=0.846 c$

And the velocity of particle moving in opposite direction with velocity 0.5 c

$v_0=\frac{u+v}{1+\frac{uv}{c^2}}$

$v_0\frac{-0.5c+0.5c}{1+\frac{0.5c\times (-0.5c)}{c^2}}=0$