How Does Recoil Affect Bullet Velocity in Physics?

[zoetrope]

For some reason, I'm having trouble getting started on 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 (velocity relative to the gun as it leaves the barrel) is $$v_{0}$$, show that the actual velocity of the bullet relative to the ground is $$\frac{v_{0}}{1+\gamma}$$ and the recoil velocity of the gun is $$\frac{- \gamma v_{0} }{1+\gamma}$$, where $$\gamma = m/M$$

If someone could point me in the right direction, I'd really appreciate it! It seems that it should be solvable using conservation of linear momentum, but the relative velocity part is throwing me off.

Thanks in advance,

zoetrope

 

[Doc Al]

If someone could point me in the right direction, I'd really appreciate it! It seems that it should be solvable using conservation of linear momentum, but the relative velocity part is throwing me off.

Welcome to PF!

The velocities are related as follows: velocity of bullet w.r.t ground = velocity of bullet w.r.t gun + velocity of gun w.r.t ground.

Express this mathematically and apply conservation of momentum from an inertial frame (the ground).

 

[zoetrope]

Thanks for the help! I guess I was just thinking too much about the problem and had made it more complex than it needed to be!

zoetrope