# A ball weighing 5 kg, moving at a speed of 3 m / s, strikes with a stationary ball, after which the balls move together.

A ball weighing 5 kg, moving at a speed of 3 m / s, strikes with a stationary ball, after which the balls move together. Determine the mass of the second ball, if the speed of the balls after impact is 2 m / s

Given:

m1 = 5 kilograms – the mass of the first ball;

v1 = 3 m / s – speed of the first ball before interaction;

v2 = 2 m / s – the speed of the balls after interaction.

It is required to determine the mass of the second ball m2 (kilogram).

Since, according to the condition of the problem, before the impact, the second ball was motionless, and after the impact they moved together, then according to the law of conservation of momentum (momentum):

m1 * v1 = (m1 + m2) * v2;

m1 * v1 = m1 * v2 + m2 * v2;

m1 * v1 – m1 * v2 = m2 * v2;

m1 * (v1 – v2) = m2 * v2;

m2 = m1 * (v1 – v2) / v2 = 5 * (3 – 2) / 2 = 5 * 1/2 = 5/2 = 2.5 kilograms.

Answer: The mass of the second ball is 2.5 kilograms.

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