A ball dropped from a height bounces back 90% of its previous height and continues its motion. If the ball travelled a distance of 190m before comes to rest, from what height the ball is dropped?

A ball dropped from a height bounces back 90% of its previous height and continues its motion. If the ball travelled a distance of 190m before comes to rest, from what height the ball is dropped? Correct Answer 10

Calculation:

The ball bounces back 90% of the previous height,

Let h be the height from which the ball is dropped.

Total distance = h + 0.9h + 0.9h + 0.9 × 0.9h + 0.9 × 0.9h + ........

⇒ h + 2 × (0.9h + 0.9 × 0.9h + ......)

⇒ h + 2 × (0.9h/(1 - 0.9)

⇒ h + 18h = 19h

⇒ 19h = 190

∴ h = 10m

Additional Information

The n^th term of a GP is given by ar^{n - 1}, where a is the first term and r is the common ratio of the GP.

Sum of n terms of GP with first term a and common ratio r is a ×  (rn - 1)/(r - 1).

The Sum of an infinite GP will be a/(1 - r).