2 balls weighing 2 kg and 4 kg. They are moving towards each other at a speed of 10 m / s

2 balls weighing 2 kg and 4 kg. They are moving towards each other at a speed of 10 m / s and 15 m / s, respectively. Determine the velocity of the balls after a non-elastic collision?

m1 = 2 kg.

m2 = 4 kg.

V1 = 10 m / s.

V2 = 15 m / s.

V -?

Since the balls interact only with each other upon impact, they can be considered a closed system of interacting bodies, for which the law of conservation of momentum in vector form is valid: m1 * V1 + m2 * V2 = m1 * V1ʼ + m2 * V2ʼ.

Where V1, V2 are the velocities of the balls before impact, V1ʼ, V2ʼ are the velocities of the balls after impact.

With an absolutely inelastic impact, the velocities of the balls after impact become the same: V1ʼ = V2ʼ = V.

For the coordinate axis, which is directed towards the motion of the second ball, the law of conservation of momentum will have the form: – m1 * V1 + m2 * V2 = (m1 + m2) * V.

V = (m2 * V2 – m1 * V1) / (m1 + m2).

V = (4 kg * 15 m / s – 2 kg * 10 m / s) / (2 kg + 4 kg) = 6.67 m / s.

Answer: after impact, the balls will move in the direction of motion of the second ball at a speed of V = 6.67 m / s.