Question

A rifleman, who together with his rifle has a mass of 100 kg, stands on a smooth surface fire 10 shots horizontally. Each bullet has a mass 10 g projected with a velocity of 800 $\frac{m}{s}$. What velocity does rifleman acquire at the end of 10 shots?

• A. -0.8 ms^-1
• B. 0.6 ms^-1
• C. 0.8 ms^-1
• D. -0.5 ms^-1

Answer 1

The correct option is A

-0.8 ms^-1

Let $m_1$ ​and $m_2$ ​be the masses of the bullet and $v_1$ ​​ and $v_2$ ​​ their respective velocities after the first shot. Initially the rifleman and the bullet are at rest, therefore initial momentum is zero. As external force is zero, momentum of the system is constant i.e initial momentum = final momentum.

$m_1$$v_1$ ​​ + $m_2$$v_2$​ = 0

$v_2$​​ = $\frac{-m_1{v}_1}{m_2}$​

$v_2$​​​ = - 0.08 $\frac{m}{s}$

Velocity acquired after 10 shots = 10 $v_2$​​​ = 10 $\times$ (-0.08) = - 0.8 $\frac{m}{s}$ i.e. the velocity of rifleman is 0.8 $\frac{m}{s}$ in a direction opposite to that of bullet.