Question

A bullet of mass 20g is horizontally fired with a velocity 150 m s^-1 from pistol of mass 2 kg. What is the recoil velocity of the pistol ?

Answer 1

The momentum conservation law states, that the momentum of the bullet is equal and opposite (in direction) to the momentum of the pistol:

$$p_b = p_p\Rightarrow m_bv_b = m_pv_p$$

where $m_b = 20g = 0.02kg, m_p = 2kg$ are masses, and $v_b = 150m/s, v_p$ and velocities of the bullet and the pistol respectively. Thus, expressing $v_p$, obtain:

$$v_p = \dfrac{m_bv_b}{m_p}\\ v_p = \dfrac{0.02kg\cdot 150m/s}{2kg} = 1.5 m/s$$

Answer. 1.5 m/s.