Drops of water fall at regular intervals from the roof of a building of height `h=16m`. The first drop striking the ground at the same moment as the fifth drop is ready to leave from the roof. Find the distance between the successive drops.

Explanation

Let the interval of time be `t_(0)`.
First drop is released at `t=0`, second drop at `t=t_(0)`, third drop at `t=2t_(0)`, fourth drop at `t=3t_(0)`, fifth drop at `t=4t_(0)`. Therefore, first first drop has fallen for time `4t_(0)`, second drop for `3t_(0)`, third drop for `2t_(0)`, fourth drop for `t_(0)` and fifth drop is about to fall. the location of drops are as shown in the figure.
`1^(st)` drop: `h_(1)=16=1/2g(4t_(0))^(2)implies 1/2 g t_(0)^(2)=1`
`2^(nd)` drop: `h_(2)=1/2g(3t_(0))^(2)=9 m`
`3^(rd)` drop: `h_(3)=1/2 g(2t_(0))^(2)=4 m`
`4^(th)` drop: `h_(4)=1/2g t_(0)^(2)=1m`
`5^(th)` drop: `h_(5)=0`
Separation between drops
`1^(st)` and `2^(nd)`: `h_(1)-h_(2)=7 m`
`2^(nd)` and `3^(rd)`: `h_(2)-h_(3)=5 m`
`3^(rd)` and `4^(th)`: `h_(3)-h_(4)=3 m`
`4^(th)` and `5^(th)`: `h_(4)-h_(5)=1 m`