After striking the floor, a certain ball rebounds (4/5)th of height from which it has fallen. Then the total distance that it travels before coming to rest, if it is gently dropped of a height of 120 m is `1260 m` b. `600 m` c. `1080 m` d. none of these

Explanation

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