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

Given, the Bullet’s mass (m₁) = 50 g

The rifle’s mass (m₂) = 4kg = 4000g

Initial velocity of the fired bullet (v₁) = 35 m/s

Let the recoil velocity be v₂.

Since the rifle was initially at rest, the initial momentum of the rifle = 0

The total momentum of the rifle and bullet after firing = m₁v₁ + m₂v₂

As per the law of conservation of momentum, the total momentum of the rifle and the bullet after firing = 0 (same as initial momentum)

Therefore, m₁v₁ + m₂v₂ = 0

The negative sign indicates that recoil velocity is opposite to the bullet’s motion