Q: If a ball is dropped from rest, it bounces from the floor repeatedly. The coefficient of restitution is 0.5 and the

speed just before the first bounce is 5 m/s . The total time taken by the ball to come to rest finally is :

(A) 1.5 s

(B) 1 s

(C) 0.5 s

(D) 0.25 s

Ans: (A)

Solution: v = 0 + gt

t = 0.5 sec

After first collision :

Speed becomes 5 (0.5) = 2.5 m/s

t_{1} = 2 (0.25) = 0.5

t_{2} = 2 (0.125) = 0.25

t_{3} = 0.125 and so on

[where t_{i} is the time taken to complete the i^{th} to and fro motion after collision]

Total time = 0.5 + [0.5 + 0.25 + 0.125 + …]

$ = 0.5 + \frac{0.5}{1-0.5} $

(Since above is a G.P. with a = 0.5 and r = 0.5)

= 0.5 + 1 = 1.5