Q34
A bouncing tennis ball is dropped from a height of 32 metre. The ball rebounds each time to a height equal to half the height of the previous bounce. The approximate distance travelled by the ball when it hits the ground for the eleventh time, is:
Answer: B
Distance covered when the ball hits the ground the first time = 32 m
The ball covers 16 + 16 = 32 m more when it hits the ground 2nd time.
The ball covers 8 + 8 = 16 m more when it hits the ground 3rd time.
And so on i.e., at the nth hit, the ball covers 32/2(n – 2) more distance.
Thus, at the 11th hit, the ball covers 32/29 m more.
Thus, the total distance the ball covers when it hits the ground 11th time
= 32 + 32(1 + ½ + ¼ + … 1/29)
= 32 + 32(1-1/210)/(1-1/2) ≈ 32 + 64
= 96 m
Hence, option (b).