Question

After striking the floor, a rubber ball rebounds to 4/5thof the height from which it has fallen. Find the total distance that it travels before coming to rest if it has been gently dropped from a height of 120 metres.

Answer 1

The first drop is 120 metres. After this the ball will rise by 96 metres and fall by 96 metres. This process will continue in the form of infinite GP with common ratio 0.8 and first term 96. The required answer is given by the formula:

a(1−r)Now,[{120(15)}+{96(15)}]=1080m