Question

A person drops a ball from an 80 m tall building and each time the ball bounces, it rebounds to p% of its previous height. If the ball travels a total distance of 320 m, then the value of p is

Answer 1

Correct Answer - 60
The ball is dropped from the heights, h=80 m.
So, initially it travels the distance of 80 m.
Then rebounds to x% of its previous height.
So, it rebounds by the distance of `(80x)/100`m and from the same height it drps again.
It continous like this till it comes to rest.
So, toatal distance travelled by the ball is
`320=80+(2xx(80x)/(100)+2xx(80x^(2))/(100^(2))+...)`
`therefore4=1+((2x)/(100)+(2x^(2))/(100^(2))+..)`
`rArr3=((2x)/100)/(1-x/100)`
`rArr3=(2x)/(100-x)`
`rArrx=60`