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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.
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Solution
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 = 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 x 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
`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.
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