A projectile weighing 20 kg flying horizontally at a speed of 50 m / s hits the platform with sand getting

A projectile weighing 20 kg flying horizontally at a speed of 50 m / s hits the platform with sand getting stuck in it. How fast will the platform begin to move if its mass is 10 tons?

Given:

m1 = 20 kilograms is the mass of the projectile;

v1 = 50 m / s – projectile speed;

m2 = 10 tons = 10 ^ 4 kilograms – platform weight.

It is required to determine the velocity of the projectile and the platform after interaction v (m / s).

According to the condition of the problem, a projectile gets stuck in a stationary platform. Then, according to the law of conservation of momentum (momentum):

m1 * v1 = (m1 + m2) * v;

v = m1 * v1 / (m1 + m2) = 20 * 50 / (20 + 10 ^ 4) =

= 1000 / (20 + 10000) = 1000/10020 = 0.01 m / s.

Answer: after being hit by a projectile, the platform will begin to move at a speed of 0.01 m / s.