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Question

A bullet of mass 20g is fired horizontally with a velocity of 150m/s from a pistol of mass 2Kg. Find the recoil velocity of the pistol.


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Solution

Step 1: Given

Mass of the bullet, m1=20g=0.02Kg

Mass of the pistol, m2=2Kg

The initial velocity of the bullet and the pistol, u1=u2=0

The final velocity of the bullet v1=150m/s

Let the recoil velocity of the pistol be v2

Step 2: Find the total momentums

According to the Law of conservation of momentum, the initial momentum will be equal to the final momentum.

The total momentum before the bullet is fired (Mi) will be zero as both the bullet and the pistol are at rest.

The total momentum after the bullet is fired (Mf) will be,

Mf=m1v1+m2v2=0.02(150)+2(v2)=3+2v2

Step 3: Equate the momentums

The Law of conservation of momentum states that the initial momentum will be equal to the final momentum.

Mf=Mi

3+2v2=0v2=-32v2=-1.5m/s

The value is negative as it is a recoil velocity. The direction of recoil velocity is opposite to the direction of motion.

Hence, the recoil velocity of the pistol is 1.5m/s.


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