# Two balls, the masses of which are 30g and 15g, move at the same speed

Two balls, the masses of which are 30g and 15g, move at the same speed of 3m / s towards each other. With what speeds will they scatter after an absolutely elastic central impact?

m1 = 30 g = 0.03 kg.

m2 = 15 g = 0.015 kg.

V1 = 3 m / s.

V2 = 3 m / s.

V “-?

Let us write the law of conservation of momentum in vector form for balls: р1 + р2 = р1 “+ р2”, where р1, р2 are the momentum of the first and second balls before impact, р1 “, р2” – momentum of balls after impact.

The momentum of the ball p is the product of the mass of the ball m by its velocity V: p = m * V.

The law of conservation of momentum in vector form will look like: m1 * V1 + m2 * V2 = m1 * V “+ m2 * V”.

Since the balls move towards each other before impact, then m1 * V1 – m2 * V2 = (m1 + m2) * V “.

V “= (m1 * V1 – m2 * V2) / (m1 + m2).

V “= (0.03 kg * 3 m / s – 0.015 kg * 3 m / s) / (0.03 kg + 0.015 kg) = 1 m / s.

Answer: V “= 1 m / s.

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