A projectile with a mass of 100 kg, flying horizontally at a speed of 500 m / s, gets into a car with sand weighing

A projectile with a mass of 100 kg, flying horizontally at a speed of 500 m / s, gets into a car with sand weighing 10 tons and gets stuck in it. What speed does a car with a projectile gain if it moved towards the projectile at a speed of 36 m / s?

Given:

m1 = 100 kilograms is the mass of the projectile;

v1 = 500 m / s – projectile speed;

m2 = 10 tons = 10,000 kilograms – the mass of a wagon with sand;

v2 = 36 meters / second – the speed of the car with sand.

It is required to determine v (m / s) – the speed of movement of the car with the projectile after interaction.

Since, according to the condition of the problem, the car with sand was moving towards the projectile, 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) = (100 * 500 – 10000 * 36) / (100 + 10000) =

= (50,000 – 360000) / 10100 = -310000 / 10100 = -30.7 m / s (the minus sign means that after interaction the car will move in the opposite direction).

Answer: the car with the projectile will move at a speed of 30.7 m / s.