Question

A 50 N gun fires a 1.0-gram bullet at a speed of 2200 m/s. What is the speed of gun recoil?

Answer 1

Let's first find the mass of the gun:

$$m_g = \dfrac{50N}{g} = \dfrac{50N}{10m/s^2} = 5kg$$

where $g = 10m/s^2$ is the gravitatinal acceleration.

The momentum of the bullet is:

$$p_b = m_bv_b = 0.001kg\times 2200m/s = 2.2\space kg\cdot m/s$$

Then, according to the momentum conservation law, the momentum of the gun has the same magnitude:

$$p_g = p_b = 2.2\space kg\cdot m/s$$

The speed of gun then:

$$v_g = \dfrac{p_g}{m_g} = \dfrac{2.2\space kg\cdot m/s }{5kg}=0.44m/s$$

Answer. 0.44 m/s.