Analytical Mechanics: bullet fired from gun problem

[swindhspectrum]

I am not quite sure how to start this problem:

A bullet of mass m is fired from a gun of mass M. If the gun can recoil freely and the muzzle velocity of the bullet is v. Show that the actual velocity of the bullet relative to the ground is v/(1+b) and the recoil velocity from the gun is -bv/(1+b), where b = m/M.

Any ideas? I understand that the velocity of the bullet with respect to the ground is equal to the velocity of the bullet with respect to the gun plus the velocity of the gun with respect to the ground. Is there some kind of a collision here?

thanks

 

[dav2008]

There is no collision but you have to realize that momentum has to be conserved, so you would treat it like any other conservation of momentum collision problem.

 

[swindhspectrum]

thanks a lot, i worked it out