Question

a projectile is fired with velocity u at an angle theta with horizontal.At the highest point of its trajectory it splits up into 3 segments of masses m ,m ,2m. First part falls vertically downward with initial velocity and second part return

Answer 1

You must be finding the velocity of other particles.
SEE, P1=P1$\sqrt[]{2UQ}$ WHERE U=M1M2/M1+M2
AND Q IS INTERNAL ENERGY.
whereas in this question, the center of mass always remain fixed.
So, it will fall where earlier it was supposed to fall.
With this info, you'll be able to do it.