A projectile weighing 30 kg flies horizontally into a trolley with sand weighing 1770 kg and gets stuck in the sand.

A projectile weighing 30 kg flies horizontally into a trolley with sand weighing 1770 kg and gets stuck in the sand. At what speed did the trolley begin to move if before the fall of the projectile it was moving at a speed of 1.5 m / s in the direction of the projectile movement?

mc = 30 kg.

Vc = 300 m / s.

Vv = 1.5 m / s.

mw = 1770 kg.

Vв “-?

Since the projectile interacts only with a trolley with sand, this system can be considered closed.

For a closed-loop system, the momentum conservation law is valid: the sum of the impulses of a closed-loop system does not change. Since the projectile sharpens in a trolley with sand, then after being hit, they will move with the same speed Vv “.

mc * Vc + mw * Vw = (mw + mc) * Vw “.

Vv “= (mc * Vc + mv * Vv) / (mv + mc).

Vw “= (30 kg * 300 m / s + 1770 kg * 1.5 m / s) / (1770 kg + 30 kg) = 6.475 m / s.

Answer: after being hit by a projectile, the trolley with sand will move at a speed Vw “= 6.475 m / s.