# Finding recoil velocity only given force and firing velocity

#### junkmonk

1. Homework Statement
A 50.0N bullet leaves a 40.0N gun with a velocity of 200. m/s. What is the recoil velocity of the gun?

2. Homework Equations
I tried to figure this out by using anything in relation to FΔt = mΔv but, I'm left with two unsolved variables, Δt and m...

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#### Dr.D

Draw a FBD for the gun and for the bullet and then write eqn of motion for each one (or impulse--momentum relations for each one).

#### junkmonk

Okay, well I can write out the impulse relations on the FBD. Since FΔt=mΔv, then F=mΔv/Δt.
SO, putting m1Δv1/Δt = m2Δv2/Δt still leaves me with the mass unavailable, they don't cancel out since they're different... How do I solve this without the mass (or time)?

I'm just getting into impulse, the only impulse equation I've learned thus far IS FΔt=mΔv, so if there's any way that it can be solved using that or that with any other combination of simple linear motion equations, it would be best understood. But if there's no other way, than I'll definately attempt to learn.

Thanks.

#### Dr.D

This is all happening some where close to the surface of the earth, I presume? You were given weights, so masses should not be too difficult to find. Pretty strange weight values, however; that is one heavy bullet!

You need to think a bit about what velocity you are given.

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