# An empty car with a mass of 20 tons runs over a resting loaded car with a mass of 60 tons and engages with it.

An empty car with a mass of 20 tons runs over a resting loaded car with a mass of 60 tons and engages with it. after coupling, the cars move at a speed of 1 m / s. what is the initial speed of an empty car.

Given:

m1 = 20 tons = 2 * 10 ^ 4 kilograms – the mass of the first car;

m2 = 60 tons = 6 * 10 ^ 4 kilograms – the mass of the second car;

v = 1 m / s – the speed of the cars after interaction.

It is required to determine v1 (m / s) – the speed of movement of the first car before interaction with the second car.

According to the problem, the first car collided with the second, and the second car was initially at rest. Then, according to the law of conservation of momentum:

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

v1 = (m1 + m2) * v / m1 = (2 * 10 ^ 4 + 6 * 10 ^ 4) * 1 / (2 * 10 ^ 4) =

= 8 * 10 ^ 4 * 1 / (2 * 10 ^ 4) = 8 * 1/2 = 8/2 = 4 m / s.

Answer: the first car (empty) was moving at a speed of 4 m / s.

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