Question

After striking a floor a certain ball rebounds `(4/5)^(t h)` of the height from which it has fallen. Find the total distance that it travels before coming to rest, if it is gently dropped from a height of `120m e t r e sdot`

Answer 1

Total distance travelled by the ball can be given as,
`S = 120+2(120*4/5)+2(120*4/5*4/5)+...oo`
`=>S = 120+2(120*4/5)[1+4/5+(4/5)^2+...oo]`
`=>S= 120+192(1/(1-4/5))`
`=>S = 120+960`
`S = 1080` m
So, total distance travelled by the ball befoe coming to rest is `1080` m.