Question

A 23 gram bullet is fired from a gun with a speed of 225m/s. If the gun has a mass of 0.7kg. What is the recoil speed of the gun?

Answer 1

According to the momentum conservation law, the momentum of the gun is equal to the momentum of the bullet (by module):

$$m_bv_b = m_gv_g$$

where $m_b = 23g = 0.023kg, m_g = 0.7kg$ are the masses of the bullet and the gun respectively, and $v_b = 225m/s, v_g$ are the velocities of the bullet and the gun respectively. Expressing $v_g$, obtain:

$$v_g = \dfrac{m_bv_b}{m_g}\\ v_g = \dfrac{0.023kg\cdot 225m/s}{0.7kg} \approx 7.4 m/s$$

Answer. 7.4 m/s.