Two balls roll towards each other at speeds of 7 and 0.5 m / s. After the collision, both balls roll towards the first

Two balls roll towards each other at speeds of 7 and 0.5 m / s. After the collision, both balls roll towards the first, whose mass is 0.4 kg, at a speed of 2 m / s. Determine the mass of the second ball.

Let us write down the law of conservation of momentum for a system consisting of two balls, the direction of the X axis is chosen to coincide with the direction of the velocity of the first ball:

m1 * v1 – m2 * v2 = v (m1 + m2), where m1 and m2 are the masses of the balls, v is the velocity after collision.

Let us express from the above equality m2:

m1 * v1 – m2 * v2 = v * m1 + v * m2;

v * m2 + v2 * m2 = m1 * v1 – m1 * v;

m2 = m1 * (v1 – v) / (v + v2).

Substituting the given values, we get:

m2 = 0.4 * (7 – 2) / (0.5 + 2) = 0.8 kg.

Answer: the mass of the second ball is 0.8 kg.