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After striking a floor a certain ball re...

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`

Text Solution

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Initially the ball falls from a height of 120 meters.
After striking the floor, it rebounds and rises to a height of `4/5xx120` meters.
Now, it falls from a height of `4/5xx4/5xx120` metres. This process is continued till the ball comes to rest.
`therefore` Total distance travelled
`=120+2[4/5xx120+(4/5)^(2)xx120+..oo]`
`=120+2[(4/5xx120)/(1-4/5)]=1080` meters
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