Question

A 10 kg mass moving at 5 m/s collides head on with a 4 kg mass moving at 2 m/s in the same direction. If e = 1/2, find their velocity after impact.

Answer 1

Given: m₁ = 10 kg, m₂ = 4 kg

u₁ = 5 m/s, u₂ = 2 m/s, e = \(\frac{1}{2}\)

To find: Velocity after impact (v1 and v2)

Formulae:

i. m₁u₁ + m₂u₂ = m₁v₁ + m₂v₂

ii. e = \((\frac{v_2-v_1}{u_1-u_2})\)

Calculation:

From formula (i),

10 × 5 + 4 × 2 = 10v₁ + 4v₂

∴ 5v₁ + 2v₂ = 29 … (1)

From formula (ii),

v₂ – v₁ = e(u₁ - u₂) = \(\frac{1}{2}\) (5 – 2) = \(\frac{3}{2}\)

∴ 2v₂ – 2v₁ = 3 … (2)

Solving (1) and (2), we have

∴ v₁ = \(\frac{26}{7}\) m/s and v₂ = \(\frac{73}{14}\) m/s

The respective velocities of the two masses are \(\frac{26}{7}\) m/s and \(\frac{73}{14}\) m/s.