Arifle with a weight of 35 n fires a 4.5-g bullet with a speed of 240 m/s. (a) find the recoil speed of the rifle in m/s. (b) if a 650-n man holds the rifle firmly against his shoulder, find the recoil speed of the man and rifle in m/s.

(a) 0.30 m/s

The total momentum of the rifle+bullet system before the shot is zero:

The total momentum of the system after the shot is the sum of the momenta of the rifle and of the bullet:

where we have

is the mass of the rifle

is the final velocity of the rifle

is the mass of the bullet

is the final velocity of the bullet

Since the total momentum must be conserved, we have

So

and so we can find the recoil velocity of the rifle:

And the negative sign means it travels in the opposite direction to the bullet: so, the recoil speed is 0.30 m/s.

(b) 0.016 m/s

The mass of the man is equal to its weight divided by the acceleration of gravity:

This time, we have to consider the system (man+rifle) - bullet. Again, the total momentum of the system before the shot is zero:

while the total momentum after the shot is

where this time we have

is the mass of the rifle+person

is the final velocity of the man+rifle

is the mass of the bullet

is the final velocity of the bullet

Since the total momentum must be conserved, we have

and so we can find the recoil velocity of the man+rifle:

So the recoil speed is 0.016 m/s.