Drop of water fall at regular intervals from roof of a building of height (H=16 m), the first drop striking the ground at the same moment as the fifth drop falls from the roof. The distances between separate drops in air as the first drop reaches the ground are.

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 drop has fallen for time `4t_(0)`, second drop for `3t_(0)`, thirs 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.

For 1st drop, `h_(1)=16=(1)/(2)g(4t_(0))^(2) rArr (1)/(2)g t_(0)^(2)=1`
For 2nd drop, `h_(2)=(1)/(2)g(3t_(0))^(2)=9 m`
For 3rd drop, `h_(3)=(1)/(2)(2t_(0))^(2)=4m`
For 4th drop, `h_(4)=(1)/(2)g t_(0)^(2) = 1m`
For 5th drop, `h_(5) = 0`
Separation between drops ltrgt 1st and 2nd : `h_(1)-h_(2)=7m`
2nd and 3rd : `h_(2)-h_(3) = 5m`
3rd and 4th : `h_(3)-h_(4) = 3m`
4th and 5 th : `h_(4)-h_(5)=1m`
Note : If the 1st drop is at the ground and the 5th drop is about to fall, the time for which the first drop has fallen `(5-1)t_(0)=4t_(0)`, where `t_(0)` is the regular interval of time.