A body moving at. 500c with respect to an observer

disintigratesinto two fragments

that move in opposite directions relative to their center

ofmass along the same line of motion as the original body.

Onefragment has a velocity of. 600c in the backward direction

relativeto the center of mass and the other has a velocity of. 500c

in theforward direction. What velocities will the observer

find?

0.8c and - 0.14c

Explanation:

The first fragment will have a speed of + 0.5c respect of a frame of reference moving at + 0.5c

Lest name v the velocity of the frame of reference, and u' the velocity of the object respect of this moving frame of reference.

The Lorentz transform for velocity is:

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

u = (0.5c + 0.5c) / (1 + (0.5c * 0.5c) / c^2) = 0.8c

The other fragment has a velocity of u' = - 0.6c respect of the moving frame of reference.

u = (-0.6v + 0.5c) / (1 + (0.5c * 0.5c) / c^2) = - 0.14c