Answer to Question #269494 in Physics for Leon Kennedy

Question

A sniper with a mass of 7 kg fires a 100 g bullet at a speed of 450 m/s. Solve for the recoil velocity of the sniper.

Answer 1

Given:

$v_1=v_2=0$

$v_2'=450\:\rm m/s$

$m_1=7\:\rm kg$

$m_2=100\:\rm g=0.1\: kg$

The law of conservation of momentum gives

$$m_1{\bf v_1}+m_2{\bf v_2}=m_1{\bf v_1'}+m_2{\bf v_2'}$$

In our case

$$0=m_1v_1'-m_2v_2'$$

$$v_1'=m_2v_2'/m_1=0.1*450/7=6.4\:\rm m/s$$