Answer:
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
