A 500 gm gun fires a 2 gm bullet with a muzzle velocity of 1600 m/s. The velocity of the gun is:

A 500 gm gun fires a 2 gm bullet with a muzzle velocity of 1600 m/s. The velocity of the gun is −6.4 m/s.

Given, $m_g=500gm=0.5kg$

mass of bullet $m_b=2gm=0.002kg$

the final velocity of the bullet $v_b=1600m{s}^{-}1$

Let $v_g$ be the final velocity of the gun

Since the gun and bullet are initially at rest, their initial velocities are $u_b=u_g=0$.

Using linear momentum conservation:  

$m_b{u}_b+m_g{u}_g=m_b{v}_b+m_g{v}_g$

$0=0.002\times 1600+0.5\times v_g$

$v_g= -6.4m/s$