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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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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.

+2 votes
by (128k points)

Mass of the rifle, m1 = 4 kg 

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

Recoil velocity of the rifle = v

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

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