Question

From a rifle of mass $4$ $kg$, a bullet of mass $50$ $g$ is fired with an initial velocity of $35$ $m{s}^{-1}$. Calculate the initial recoil velocity of the rifle.

Answer 1

The rifle and the bullet make a system. Since, there is no external force acting on it the momentum of the system should be conserved.
$\therefore m_1{u}_1+m_2{u}_2=m_1{v}_1+m_2{v}_2$
$\Rightarrow 4\times 0+\left(\frac{50}{100}\right)\times 0=4v+\frac{50}{1000}\times 35$
$\Rightarrow 4v=-\frac{35}{20}$
$\Rightarrow v=-\frac{35}{80}$ $m/s$
Note:- Negative sign indicates that recoil velocity is opposite to the motion of the bullet.