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 = V_{2}′ - V_{1}′ = 5 × e = 3 m / sec
Using principle of conservation of momentum
m_{1} V_{1}′ + m_{2} V_{2}′ = m_{1} V_{1 } + m_{2} V_{2 }---------(A)
10 V_{1}′ + 4 V_{2}′ = 100 + 20 = 120 --------- (B)
Solving out Eqs. (A) and (B)
10 V_{1}′ + 4 (3 + V_{1}′) = 120
14 V_{1}′ = 108
or,
V_{1}′ = 7.71 m / sec
V_{1} = 10 m / sec
∴ V_{2}′ = 3 + V_{1}′ = 10.71 m / sec .
While V_{2} = 5 m / sec