A cart with mass m moves at a speed of 3V and catches up with a cart with a mass of 3m

A cart with mass m moves at a speed of 3V and catches up with a cart with a mass of 3m and moving in the same direction at a speed V. What is the modulus of the speed of the carts after their inelastic interaction?

Given:

m1 = m is the mass of the first cart;

v1 = 3 * v – speed of the first cart;

m2 = 3 * m – mass of the second cart;

v2 = v is the speed of the second cart.

It is required to find the velocity v3 after inelastic interaction.

According to the law of conservation of momentum:

m1 * v1 + m2 * v2 = (m1 + m2) * v3, hence

v3 = (m1 * v1 + m2 * v2) / (m1 + m2) = (m * 3 * v + 3 * m * v) / (m + 3 * m) = 6 * m * v / 4 * m = 1.5 * v.

Answer: the speed after inelastic interaction will be equal to 1.5 * v.