Question

From a rifle of mass 4 kg, a bulle of mass 50 g is fired with an initial velocity of 35 m s^-1. What is the the initial recoil velocity of the rifle?

Answer 1

0.4375 m/s.

Explanation:

Assuming there are no external forces to the system, then the total linear momentum `p` must be the same before and after the bullet was fired.

Since `p = mv`, where `m` and `v` are the mass and velocity of a body with momentum `p`, then prior to the bullet being fired, both rifle and the bullet itself are at rest, which means that `p_(before) = 0`.

From momentum conservation, then, `p_(after) = 0`. Therefore:

`m_(b)v_(b) + m_rv_r= 0`, where the indices 'b' and 'r refer to the bullet and the rifle, respectively.

Then:

`50 * 10^-3 *35 + 4*v_r = 0`;

`1,75 + 4*v_r = 0`;

`v_r = -0.4375 m/s`.

Note that the minus signal indicate that the rifle's velocity is opposite to the one of the bullet.