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Question 3
From a rifle of mass 4 kg, a bullet of mass 50 g is fired with an initial velocity of 35 ms1 . Calculate the initial recoil velocity of the rifle.

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Solution

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 ms1
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=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=1.754=0.4375 ms1
The negative sign indicates that the rifle recoils backwards with a velocity of 0.4375 ms1

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