Question

A 5.5 kg rifle fires an 11 g bullet with a velocity of 1000 m/s.

(a)   What is the recoil velocity of the rifle?

(b)  If the shooter holds the rifle firmly against his shoulder, what will be the recoil velocity? Assume the mass of the shooter is 120 kg.

Answer 1

a)

$$p_i=p_f=0,$$ $$Mv_{rec}+m_bv_b=0,$$ $$v_{rec}=-\dfrac{m_bv_b}{M}=-\dfrac{0.011\ kg\cdot1000\ \dfrac{m}{s}}{5.5\ kg}=-2\ \dfrac{m}{s}.$$

The sign minus means that the recoil velocity of the riffle directed in the opposite direction to the motion of the bullet.

b)

$$v_{rec}=-\dfrac{m_bv_b}{M}=-\dfrac{0.011\ kg\cdot1000\ \dfrac{m}{s}}{120\ kg+5.5\ kg}=-0.9\ \dfrac{m}{s}.$$

The sign minus means that the recoil velocity of the riffle directed in the opposite direction to the motion of the bullet.