Question

A ball is dropped from height of 100 feet towards the ground. It hits the ground and bounces back 80% of the fall. This continues till the ball comes to rest. Find the vertical distance covered by the ball

Answer 1

the height on the nth bounce is 100*0.8^n

So, the geometric sequence for the bounces is
a = 100
r = 0.8

Each bounce is a round trip, except for the 0th trip, so the distance traveled is

2*100/0.2 - 100 = 900 ft

The real-world distance of course will be slightly less than that.