Physic Problem

[JustAnotherDay]

Any people good at physics here? I'm stuck with a problem no one seems to know how to solve:


Prove that the center of mass of a torn grenade at any time since the explosion covers with the center of mass before the explosion

[auto]

well that's pretty simple the center of mass will be in the same place as before due to newtons 2nd law F=ma
Sorry I don't know how to prove this but it should be enough to say that due to the laws of conservation of momentum the center of mass will be exactly the same as before.

[JustAnotherDay]

The whole point of the problem is to prove it algebraically, if someone can prove this before 9.00 CET I'll even pay you 250 tibia coins :D

[auto]

I hope this isnt for a class because I don't think you understand the basic concept here.
If the grenade weighs 2kg and blew up and for simplicity we will say there are 2 bits of shrapnel that must conserve momentum and cancel eachother by F=ma. That is to say a piece might blast off to the left with a mass of 2kg and a speed of 100m/s where to the right a 1kg piece travels at a speed of 200m/s and thus these both cancel eachother out.
2*100 = 200N Left
1*200 = 200N Right