Find the Ratio: Solving Recoil Speed in Homework Equations

[agadag]

Homework Statement

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 13-g bullet is shot forward with a speed of 290 m/s, and the person recoils with a speed of vc. When a blank cartridge is used , a mass of 0.13g is shot forward with a speed of 53 m/s , and the recoil speed is vb. Find the ratio vb/vc.

Homework Equations

I tried to use P= p₁+p₂
I got
P₁=13*V_c
P₂=.13*V_b
Ended with 13V_c+.13V_b
I am sooo confused. Its asking for the ratio and its totally throwing me off. Plus I am not even sure I am using the right formula or if I understand the question properly

The Attempt at a Solution

 

[rl.bhat]

Initially person and the gun are at rest.So the total momentum of the system is zero.
When the gun is fired, bullet moves forward with some velocity and person recoils. Find the momentum of each and add them. According to the law conservation of momentum the sum should be zero.
Write down two equations, one for standard cartridge and other for blank cartridge. Then find of vc and vb.

 

[agadag]

Im sorry, I don't understand. I am a beginner at physics and don't have a good basis. Was I on the right track. If not, can you demonstrate what ur saying

 

[agadag]

nevermind...got it