Abody 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

it is called kinetic energy