Question

27. The boy with mass m1 = 52kg is located on the cart with mass m2 = 20kg and from the resting position he shoots horizontally. The mass of lead is m0 = 120g, while v0 = 800m / s. Determine the speed that the cart has taken after five shots. Friction forces are absent.

Answer 1

According to the law of conseration of linear momentum, we get:

$$p_i=p_f,$$ $$(m_1+m_2)v_{cart}+5m_0v_0=0,$$ $$(m_1+m_2)v_{cart}=-5m_0v_0$$ $$v_{cart}=\dfrac{-5m_0v_0}{(m_1+m_2)},$$ $$v_{cart}=\dfrac{-5\cdot0.12\ kg\cdot800\ \dfrac{m}{s}}{(52\ kg+20\ kg)}=-6.7\ \dfrac{m}{s}.$$

The sign minus means that the cart moves in the opposite direction to the motion of the bullets.