A ball of 0.1 kg makes an elastic head on collision with another ball

1.	A ball of 0.1 kg makes an elastic head on collision with another ball of unknown mass at rest. If the first ball rebounds at one third of its initial speed, what is the mass of the other ball?
Answer» m₁ = 0.1 kg, m₂ = ? u₂ = 0, v₁ = -1/3 u₁ v₁ = {(m₁ + m₂)u₁}/{m₁ + m₂} + {2m₁v₂}/{m₁ + m₂} or, -u₁/3 = {(0.1 - m₂)u₁}/{0.1 + m₂} + 0 or, -1/3 = {0.1 - m₂}/{0.1 + m₂} or, -0.3 + 3m₂ = 0.1 + m₂ or, 2m₂ = 0.1 + 0.3 = 0.4 or, m₂ = 0.4/2 = 0.2 kg

A ball of 0.1 kg makes an elastic head on collision with another ball of unknown mass at rest. If the first ball rebounds at one third of its initial speed, what is the mass of the other ball?

Answer»

m₁ = 0.1 kg, m₂ = ?

u₂ = 0, v₁ = -1/3 u₁

v₁ = {(m₁ + m₂)u₁}/{m₁ + m₂} + {2m₁v₂}/{m₁ + m₂}

or, -u₁/3 = {(0.1 - m₂)u₁}/{0.1 + m₂} + 0

or, -1/3 = {0.1 - m₂}/{0.1 + m₂}

or, -0.3 + 3m₂ = 0.1 + m₂

or, 2m₂ = 0.1 + 0.3 = 0.4

or, m₂ = 0.4/2 = 0.2 kg