Question

Find an expression for the recoil velocity of a gun when it fires a bullet

Answer 1

When a bullet is fired from a gun,the gun moves back,opposite to the direction of motion of the bullet.This backward motion of the gun is called recoil and the velocity with it moves back is called recoil velocity.Before firing the bullet,both the bullet and the gun are at rest.Hence,the total momentum is zero.After firing the bullet,the bullet moves forward with a large momentum and the gun moves backward with equal momentum.

Let m and M be the masses of the bullet and gun respectively.If v and V are the velocities of the bullet and gun respectively after the firing,then

0 = mv + MV

therefore V = - mv/M

This is the expression for recoil velocity of the gun.The negative sign indicates that the gun moves in a direction to that of the bullet
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Answer 2

V= -(mv)/M

Explanation:

Consider a gun with mass 'M' firing a bullet of mass 'm' with a muzzle speed 'V' . Let it triggers with a recoil velocity 'v' . Then according to the law of conservation of linear momentum , momentum before firing = momentum after firing .

0=mv+MV

MV= -(mv)

V= -(mv)/M