A ball weighing 3 kg moving at a speed of 2 m / s. hits a stationary ball.

A ball weighing 3 kg moving at a speed of 2 m / s. hits a stationary ball. After the impact, the balls flew in different directions at the same speed of 1 m / s. Find the mass of the second ball.

m1 = 3 kg.

V1 = 2 m / s.

V2 = 0 m / s.

V1 “= V2” = 1 m / s.

m2 -?

For a closed system of balls, the law of conservation of momentum is valid in vector form: 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” – the speed of the balls after impact.

Since the second ball was immovable, then V2 = 0 m / s.

m 1 * V1 = m 1 * V1 “+ m2 * V2”.

We direct the ОХ axis towards the movement of the first ball before the impact.

OH: m 1 * V1 = – m 1 * V1 “+ m2 * V2”.

m2 * V2 “= m 1 * V1” + m 1 * V1.

The formula for determining the mass of the second ball m2 will be: m2 = m 1 * (V1 “+ V1) / V2”.

m2 = 3 kg * (1 m / s + 2 m / s) / 1 m / s = 9 kg.

Answer: the second ball has a mass m2 = 9 kg.