Gun Recoil

## Question:

The question is about the recoiling situation in a gun. My
teacher says the recoil velocity V = -mv/M.
What are m & M. Is m mass of the object which moves
forward while M is the object which recoils? Or is it vice
verser?

For small guns such as those ladies' silver small gun,
they are small in size. Powerful guns such as those which break
metals, they are larger in size. And for those which can shoot
bullets continuously, they are even larger in size. Some are too
large to be hold in arm and they have to be set on a stand.

How is the size of the guns related to the recoil velocity? Is
it for large size, mass will be large, as V=-mv/M, if M is large,
recoil velocity is small?

Thanks again for your precious answers!

## Answer:

The gun recoil is an example of the conservation of momentum.
Before the shot, both the bullet and the gun are at rest so the
total momentum is zero. After the shot the bullet is traveling in
one direction and the gun in the opposite direction such that the
total momentum remains zero. Let M be the mass of the gun and m
be the mass of the bullet. Let v be the velocity of the bullet
and V be the velocity of the gun. From the conservation of
momentum we know that MV+mv=0. Subtracting mv from
both sides of this equation gives us MV=-mv.
Dividing by the mass of the gun (M) gives us V=-mv/M
which is the equation you presented. So M must be the mass of the
gun in your equation.
You are exactly correct in your analysis of how the size of
the gun is related to recoil velocity.