Does each fragment get half the momentum when a shell explodes?

[Weather Freak]

Hey folks, I have this problem as part of my weekly homework:

A shell is shot with an initial velocity of 20 m/s, at an angle of 60 degrees with the horizontal. At the top of the trajectory, the shell explodes into two fragments of equal mass. One fragment, whose speed immediately after the explosion is zero, falls vertically...

The rest of the problem isn't important to my question, which is this: I know that momentum is conserved. If the shell has momentum P right before it splits in half, does each half now have momentum P or does each shell have momentum 1/2 P? If each shell has momentum P, does that mean that since the mass goes down in the shell that is not dropping, that the velocity must increase to make up for the difference?

Thanks!

 

[Päällikkö]

Write the equations for conservation of momentum. If the final velocity of say fragment one is 0, what can you say about fragment two's final velocity?

 

[Weather Freak]

Hmm... so the total momentum of the two pieces must equal the momentum of the first piece before it exploded?

 

[Päällikkö]

Yes. There are no external forces acting, only internal.

 

[Weather Freak]

Thank you!