#### Question

From a rifle of mass 4 kg, a bullet of mass 50 g is fired with an initial velocity of 35 m s^{−1}. Calculate the initial recoil velocity of the rifle.

#### Solution

Mass of the rifle, m_{1} = 4kg

Mass of the bullet, m_{2} = 50g = 0.05 kg

Recoil velocity of the rifle = v_{1}

Bullet is fired with an initial velocity, v_{2} = 35 m/s

Initially, the rifle is at rest.

Thus, its initial velocity, *v* = 0

Total initial momentum of the rifle and bullet system (m_{1} + m_{2})v = 0

Total momentum of the rifle and bullet system after firing:-

= m_{1}v_{1} + m_{2}v_{2} = 4(v_{1}) + 0.05 x 35 = 4v_{1} + 1.75

According to the law of conservation of momentum:

Total momentum after the firing = Total momentum before the firing

4v_{1} + 1.75 =0

`v_1 = 1.75/4 =-0.4375" m/s"`

The negative sign indicates that the rifle recoils backwards with a velocity of 0.4375 m/s.