Two railway platforms move towards each other at speeds of 1.2 km / h and 1.8 km / h.

Two railway platforms move towards each other at speeds of 1.2 km / h and 1.8 km / h. The mass of the first platform is 16 tons, the mass of the second platform is 24 tons. At what speed and in what direction will the platforms move after they are connected?

M1 = 16 tons = 16,000 kilograms – the mass of the first platform;

v1 = 1.2 km / h = 0.3 m / s – the speed of the first platform;

M2 = 24 tons = 24000 kilograms – the mass of the second platform;

v2 = 1.8 km / h = 0.5 m / s – the speed of the second platform.

It is required to determine with what speed v (m / s) and in what direction the platforms will move after clutching.

Let the first platform move in the positive direction of the coordinate axis, and the second platform in the negative direction. Then, according to the law of conservation of momentum:

M1 * v1 – M2 * v2 = (M1 + M2) * v;

v = (M1 * v1 – M2 * v2) / (M1 + M2) = (16000 * 0.3 – 24000 * 0.5) / (16000 + 24000) =  (4800 – 12000) / 40000 = -7200 / 40000 = -0.18 m / s (the minus sign means that the speed will be directed to the negative side of the coordinate axis).

Answer: the platforms after clutching will move at a speed of 0.18 m / s, in the direction of movement of the second platform.