# Thread: Help with bouncing ball

1. ## Help with bouncing ball

Hi, anyone out there, my problem is pure logic that I obviously don't have at the mo.........

A ball bounces everytime at 2/5 of the height of its bounce. If we let it fall 75 cm, calculate the height it reaches on the 2nd bounce.

Please someone help me make sense of this

2. Originally Posted by Asnera
A ball bounces everytime at 2/5 of the height of its bounce. If we let it fall 75 cm, calculate the height it reaches on the 2nd bounce.
...
Hello, Asnera,

The ball starts at a height of 75 cm. The height after the first bounce is (2/5)*75 cm = 30 cm. The height after the seconf bounce is (2/5)*30 cm = 12 cm.
In general: Let n be the number of bounces and h the height with respect of n then:
$h(n)=75cm \cdot \left(\frac{2}{5}\right)^n$

EB