# Finding recoil speed given force, mass, and velocity

• mandy9008

## Homework Statement

A rifle with a weight of 25 N fires a 5.5 g bullet with a speed of 260 m/s.
(a) Find the recoil speed of the rifle.
(b) If a 725 N man holds the rifle firmly against his shoulder, find the recoil speed of the man and rifle.

p=mv
F=p/t

## The Attempt at a Solution

I do not even know where to begin converting the mass to 0.0055 kg

Hint: What's conserved as the rifle is fired?

momentum?

momentum?
Yep. That's all you need to solve both parts.

m1v1i + m2v2i = m1v1f + m2v2f

m1v1i + m2v2i = m1v1f + m2v2f
Sure. What's the initial velocity and momentum before the rifle is fired?

velocity and momentum is 0

velocity and momentum is 0
Right. Keep going. You're given the final speed of the bullet.

okay, so it will be
mass 1 is 0.0055kg? then what is mass 2?

okay, so it will be
mass 1 is 0.0055kg? then what is mass 2?
Mass 2 is the mass of the rifle (at least in part a). You'll have to figure that out from the given information.

okay, so
m1v1i + (0.0055 kg) (0 m/s) = m1v1f + (0.0055 kg) (260 m/s)

I am confused now

okay, so
m1v1i + (0.0055 kg) (0 m/s) = m1v1f + (0.0055 kg) (260 m/s)

I am confused now

You know weight of the rifle. Find mass of the rifle.
Before firing, rifle and bullet haven't moved yet. You can consider their velocities before firing.

I suggest you write out all your equations and develop them before putting numbers in. Things are less messy then and thus more elegant.

okay, so
m1v1i + (0.0055 kg) (0 m/s) = m1v1f + (0.0055 kg) (260 m/s)

I am confused now
You switched them around. You have m2 as the mass of the bullet, which means that m1 is the mass of the rifle (for part a). That's fine.

You are given the weight of the rifle in Newtons, so what's its mass?

Since the initial speed of everything is zero, what does that do to the left hand side of your equation?