Find the Ratio of Recoil Velocities: Blank vs Standard Cartridge

[cstout]

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 14-g bullet is shot forward with a speed of 270 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

vb/vc

The Attempt at a Solution

i simply tried mass(velocity) for each one and did vb/vc to get .0018 but the answer is not right. I'm not sure if i have an error or if those are the wrong steps

 

[tony873004]

Use conservation of momentum. P=mv.

 

[cstout]

for the first part P = 3.78 kgm/s (converting 14g to kg) and the second part is P = .00689 kgm/s(also converting .13g to kg) and I divided (.00689/3.78) to get .0018 again. Or is there a step in between that I am missing

 

[blochwave]

All you're doing is dividing the momentums of the bullets after being fired by each other.

Instead you need to use conservation of momentum to find the recoil speeds in each case. A problem is that the gun's mass is unknown, but when you take the ratios of the two speeds the mass will cancel

 

[cstout]

what would you use to find the recoil speeds then?

 

[blochwave]

Conservation of momentum

initially the momentum before firing is 0. Then you fire and the bullet is going one way with such and such momentum, and the gun is going the other way, so you can find the necessary momentum so that the total is still 0 like it was initially