Question

Derive the recail velocity of gun​

Answer 1

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Be the velocity of the bullet and be the velocity of the gun. Now the initial momentum of the gun and the bullet will be zero. After the gun is fired at that moment final momentum will be equal to the momentum of the gun and momentum of the bullet. Therefore, the recoil velocity of the gun is −mvM.

Answer 2

Answer:

V = -(m×v)/M

where m = mass of bullet fired from the gun

           v = velocity of bullet

            M = mass of the gun

Explanation:

When a bullet is fired from the gun , the gun recoils with some velocity due to the momentum created in the gun by the bullet.

Let the mass of bullet fired from gun be 'm' and mass of gun be 'M'.

Also let velocity of bullet be 'v' and recoil velocity of gun 'V'

Initial Momentum = 0 since both gun and bullet are at rest

Final Momentum = p(gun) + p(bullet)           [Momentum = Mass × Velocity]

According to principle of conservation of Linear momentum,

Initial Momentum = Final Momentum

0 = m × v + M × V

-(m × v) = M × V

therefore, V = -(m×v)/M     [ negative sign indicates that gun recoils(moves)  

                                             in the  opposite direction of the bullet ]

This is the formula for recoil velocity (V) of the gun.