A gun is installed on a stationary railway platform. The mass of the platform with the gun is 15 tons.

A gun is installed on a stationary railway platform. The mass of the platform with the gun is 15 tons. The gun shoots at an angle of 60 degrees to the horizon. With what speed will the platform roll if the mass of the projectile is 20 kg and it flies out at a speed of 600 m / s?

m = 15 tons = 15,000 kilograms – the mass of the platform with the tool;

a = 60 ° to the horizon – the angle to the horizon at which the gun shoots;

v0 = 600 m / s (meters per second) – projectile speed;

m0 = 20 kilograms is the mass of the projectile.

It is required to determine v (m / s) – the speed with which the platform will move.

Since the mass of the platform with the weapon is much less than the mass of the projectile that has flown out, we consider the mass of the weapon and the platform without the projectile to also be equal to m.

Then, according to the law of conservation of momentum (momentum):

m0 * v0 * cos (a) = m * v, from here we find that:

v = m0 * v0 * cos (a) / m = 20 * 600 * 0.5 / 15000 = 6000/15000 = 6/15 = 0.4 m / s.

Answer: The platform will roll at a speed of 0.4 m / s.