Speed of person firing gun on ice

[mikefitz]

A person is standing on a sheet of ice so slippery that friction may be ignored. This individual fires a gun parallel to the ground. When a standard cartridge is used , a 17-g bullet is shot forward with a speed of 250 m/s, and the person recoils with a speed of vc. When a blank cartridge is used , a mass of 0.17g is shot forward with a speed of 57 m/s , and the recoil speed is vb. Find the ratio vb/vc.

I'm trying to figure out how to apply the conversation of momentum to this problem. I know that Pi = Pf, but in the case of this problem how would I figure out what 'recoil speed' the person experiences? Please help me begin this problem, thanks!

 

[neutrino]

You don't need to find the speeds, only their ratio is required. Use Pi = Pf in both cases, and then divide one equation by the other.