A car with a mass of 15 tons, moving at a speed of 50 cm / s, is catching up with another car with a mass of 10 tons

A car with a mass of 15 tons, moving at a speed of 50 cm / s, is catching up with another car with a mass of 10 tons, which is moving at a speed of 30 cm / s. What will be the speed of the cars after the coupling is triggered?

Given:

m1 = 15 tons = 15,000 kilograms – the mass of the first car;

v1 = 50 cm / s = 0.5 m / s (meters per second) – the speed of the first carriage;

m2 = 10 tons = 10,000 kilograms – the mass of the second car;

v2 = 30 cm / s = 0.3 m / s is the speed of the second car.

It is required to determine v (m / s) – the speed of the cars after coupling (interaction).

According to the condition of the problem, both cars move in the same direction before interaction. We also believe that the interaction of the cars was absolutely inelastic. Then, according to the law of conservation of momentum (momentum), we obtain:

m1 * v1 + m2 * v2 = (m1 + m2) * v;

v = (m1 * v1 + m2 * v2) / (m1 + m2);

v = (15000 * 0.5 + 10000 * 0.3) / (15000 + 10000) = (7500 + 3000) / 25000 =

= 10500/25000 = 10.5 / 25 = 0.42 m / s.

Answer: after interaction, the speed of movement of both cars will be equal to 0.42 m / s.