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.

Answer 1

Mass of the rifle, m₁ = 4kg

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

Recoil velocity of the rifle = v₁

Bullet is fired with an initial velocity, v₂ = 35m/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 x 35 = 4v₁ + 1.75

According to the law of conservation of momentum:

Total momentum after the firing = Total momentum before the firing

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

Answer 2

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