calculate the final velocities of the two massesa

Question

Calculate the final velocities of the two masses:

A mass of 10 kg moving along with a velocity of 10 m/sec along x direction follows another mass of 4 kg moving with 5 m/sec in the similar direction. Calculate the final velocities of the two masses if e = 0.6.

Solution

Velocity of approach = 10 - 5 = 5 m / sec

∴ Velocity of separation = V₂′ - V₁′ = 5 × e = 3 m / sec

Using principle of conservation of momentum

m₁ V₁′ + m₂  V₂′ = m₁ V₁  + m₂  V₂                               ---------(A)

10 V₁′ + 4 V₂′ = 100 + 20 = 120                        --------- (B)

 Solving out Eqs. (A) and (B)

10 V₁′ + 4 (3 + V₁′) = 120

14 V₁′ = 108

or,

V₁′ = 7.71 m / sec

V₁  = 10 m / sec

∴ V₂′ = 3 + V₁′ = 10.71 m / sec .

While       V₂  = 5 m / sec