A ball is dropped from a height of 80 metres. After hitting the ground, it bounces back to 60% of the height from which it fell. It continues bouncing in this way—each time rising to 60% of the previous height. (i) What height does the ball reach after the bounce? (ii) What is the total vertical distance the ball has travelled by the time it hits the ground for the time?
6.2208 metres
301.3376 metres
Explanation
The sequence of maximum heights attained by the ball after each bounce forms a Geometric Progression (GP). The first term is the height after the first bounce, and the common ratio is the bounce-back percentage. The height after the 5th bounce is the 5th term of this GP. The total vertical distance is the sum of the initial drop and twice the sum of the heights of the first 5 bounces, as the ball travels both up and down for each bounce before the 6th hit.