When fired from an air rifle, a bullet of mass m is fired at a velocity v. What modulus of momentum

When fired from an air rifle, a bullet of mass m is fired at a velocity v. What modulus of momentum does an air rifle acquire after firing if its mass is 150 times greater than a bullet?

Given:

v – bullet velocity when fired from an air rifle;

m is the mass of the bullet;

M = 150 * m is the mass of the air rifle.

It is required to determine the impulse of the air rifle P1.

Let us introduce a coordinate system, the OX axis of which is directed towards the bullet exit. Then, the momentum of the bullet P will have a positive value, and the momentum of the rifle P1 will be negative, since as a result of the recoil, the rifle will move backward. According to the law of conservation of momentum (momentum):

-P1 + P = 0;

P1 = P;

P1 = m * v.

Answer: the rifle gains momentum equal to m * v