Dear Student,
Initial velocity, u = 147 m/s
Now the lift starts moving up with constant velocity, vlift = 5 m/s
Relative initial velocity of the ball w.r.t. the boy is,
u/ = net upward velocity of the ball – net upward velocity of the boy = (147 + 5) – 5 = 147 m/s
Relative final velocity of the ball w.r.t. the boy (as the ball comes back to the hand) is,
v/ = net upward velocity of the ball – net upward velocity of the boy
=> v/ = (-147 + 5) – 5 = -147 m/s
The acceleration due to gravity is same, g = -9.8 m/s2
The time taken by the ball to come back to hand is, t = (v – u)/g
=> t = (-147 – 147)/(-9.8)
=> t = 30 s