A ball weighing 0.2 kg moves at a speed of 9 m / s, collides with a stationary ball whose mass is 0.1 kg.

A ball weighing 0.2 kg moves at a speed of 9 m / s, collides with a stationary ball whose mass is 0.1 kg. What are the velocities of the balls after the collision, if the collision is central and the impact can be considered absolutely elastic?

m1 = 0.2 kg.

V1 = 9 m / s.

m2 = 0.1 kg.

V2 = 0 m / s.

V1 “-?

V2 “-?

Let’s use the law of conservation of momentum: m 1 * V1 + m2 * V2 = m 1 * V1 “+ m2 * V2”, where m 1, m2 are the masses of the balls, V1, V2 are the velocities of the balls before impact, V1 “, V2” are the velocities balls after impact.

m 1 * V1 = m 1 * V1 “+ m2 * V2”.

Let’s write down the law of conservation of total mechanical energy: m 1 * V1 ^ 2/2 = m 1 * V1 ^ “2/2 + m2 * V2 ^” 2/2.

V1 “= (m1 – m2) * V1 / (m1 + m2).

V2 “= 2 * m1 * V1 / (m1 + m2).

V1 “= (0.2 kg – 0.1 kg) * 9 m / s / (0.2 kg + 0.1 kg) = 3 m / s.

V2 “= 2 * 0.2 kg * 9 m / s / (0.2 kg + 0.1 kg) = 12 m / s.

Answer: V1 “= 3 m / s, V2” = 12 m / s.