A platform with sand with a total mass of M = 2t stands on rails on a horizontal track section.

A platform with sand with a total mass of M = 2t stands on rails on a horizontal track section. A shell with a mass of m = 8 kg gets into the sand and gets stuck in it. Neglecting friction, determine with what speed the platform will move if, at the moment of impact, the speed of the projectile is v = 450 m / s, and its direction is from top to bottom at an angle α = 30 ° to the horizon.

M = 2 t = 2000 kg.

m = 8 kg.

∠α = 30 °.

Vsn = 450 m / s.

V “-?

For a closed system of bodies of a projectile and a platform with sand, the law of conservation of momentum in vector form is valid: M * Vpl + m * Vsn = (M + m) * V “.

Where M * Vpl is the impulse of the platform before the projectile hits, m * Vsn is the impulse of the projectile before hitting the platform, (M + m) * V “is the impulse of the platform with the projectile after being hit.

Since the platform was at rest, Vpl = 0 m / s.

m * Vсн = (M + m) * V “.

For projections on the horizontal axis, the law of conservation of momentum will take the form: m * Vsn * cosα = (M + m) * V “.

V “= m * Vсн * cosα / (M + m).

V “= 8 kg * 450 m / s * cos30 ° / (2000 kg + 8 kg) = 1.55 m / s.

Answer: after being hit by a projectile, the speed of the platform with sand will become V “= 1.55 m / s.