Question 3

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

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

Total mass = m₁ + m₂ = 4 + 0.05 = 4.05 kg

Since the system was at rest , velocity (v) = 0

Momentum ( before firing ) = mass x velocity = ( m₁ + m₂ )v = ( 4.05 ) 0 = 0 kg m/s

Total momentum = momentum of bullet + momentum of rifle = m₁ v₁ + m₂ v₂

= 0.05 x 35 + 4 x v2 = 7/4 + 4 v2

Since the total momentum remain conserved

Total momentum before firing = Total momentum after firing

0 = 7/4 + 4 v₂

4 v₂ = - 7/4

v₂ = - 7/16

v₂ = -04375 m/s

Thus , the recoil velocity of the pistol is -0.4375 m/s .

The negative sign of velocity means that the rifle will recoil in the opposite direction of the bullet.

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