Two carts are going towards each other on a smooth horizontal surface. One of them has a mass of 5kg and moves

Two carts are going towards each other on a smooth horizontal surface. One of them has a mass of 5kg and moves at a speed of 1m / s. The mass of the second cart is 0.5 kg. With what speed did it move if, after the impact, the heavy cart stopped, and the speed of the light cart remained the same in magnitude, but changed direction to the opposite?

Given:
m1 = 5 kilograms – the mass of the first cart;
v1 = 1 meter per second – speed of the first cart;
m2 = 0.5 kilograms – the mass of the second cart.
It is required to determine the speed of the second carriage v2 (meter per second).
According to the problem, the first cart stopped after the impact, and the speed of the second cart remained the same, but changed its direction. Let initially the first cart move in the positive direction of the coordinate system, and the second cart — in the negative direction. Then, according to the law of conservation of momentum:
m1 * v1 – m2 * v2 = m2 * v2;
m1 * v1 = m2 * v2 + m2 * v2;
m1 * v1 = 2 * m2 * v2;
v2 = m1 * v1 / (2 * m2) = 5 * 1 / (2 * 0.5) = 5/1 = 5 m / s.
Answer: the speed of the second cart was 5 m / s.