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.

Mass of the rifle, m₁ = 4 kg

Mass of the bullet, m₂ = 50g = 0.05 kg

Recoil velocity of the rifle = v₁

Bullet is fired with an initial velocity, v₂ = 35 m/s

Initially, the rifle is at rest.

Thus, its initial velocity, v = 0

Total initial momentum of the rifle and bullet system = (m₁ + m₂)v = 0

Total momentum of the rifle and bullet system after firing:

= m₁v₁ + m₂v₂ = 4(v₁) + 0.05×35 = 4v₁ + 1.75

According to the law of conservation of momentum:

Total momentum after the firing = Total momentum before the firing

4v₁ + 1.75 = 0

⇒ v₁ = – 1.75/4 = – 0.4375 m/s

The negative sign indicates that the rifle recoils backwards with a velocity of

0.4375 m/s.