Calculating Momentum of Gun-Fired Shell

[Oblio]

Using the conservation of momentum I need to show that a gun firing a shell will equal:

v=v(1+m)M

Where the gun of mass M shoots a shell with mass m and a velocity of v.
There are no external forces, ie the gun is free to recoil.
And its the velocity with respect to the ground...

This is what I've gotten to

v(m +M) = Mv(s) - mv(g)

v=Mv(s) - mv(g) / (m + M)
I'v done more, but I'm not if need to equal something to zero somewhere, since technically v (initial) is zero...

help?

 

[learningphysics]

What exactly is the question asking... if the initial velocity of the system is 0, then the initial momentum of the system is 0.

So: initial momentum = final momentum

0 = Mbullet*vbullet - Mgun*vgun