physics

In an elastic head on collision, a ball of mass 1kg moving a 4m/s collides with a stationary ball of mass 2kg. Calculate the velocities of the balls after the collision, indicating the direction in which they are travelling.

 

m.Va₁ + 2m.0 = mVa₂ + 2mv_b

or, Va₁ = Va₂ + 2V_b

or, Va₁ - Va₂ = 2V_b ------------------- (1)

Energy conservation

½ m.Va₁² + ½ 2m.0² = ½ m.Va₂² + ½ 2m.V_b²

Or Va₁² = Va₂² + 2.V_b²

Or, (Va₁ – Va₂)(Va₁ + Va₂) = 2 V_b²     ------------------ (2)

Substituting (1) in (2) we get

2 V_b (Va₁ + Va₂) = 2V_b²

Or, (Va₁ + Va₂) = V_b -------------------------(3)

Equating (1) and (3), we get

2Va₁ = 3V_b

Or, V_b = 2/3 Va1

And Va₂ =  V_b – Va₁ = 2/3 Va₁ – Va₁ = - 1/3 Va₁

Substituting Va₁ = 4 m/s, we get

Va₂ = - 4/3  m/s and V_b = 8/3