Drops of water fall at regular intervals from the roof of a building of height 16 m. The first drop strikes the ground at the same moment as the fifth drop leaves the roof. Find the distances between successive drops.

Explanation

Step-i: Time taken by the first drop to touch the ground =t=`sqrt((2h)/g)`
For h=16m , `t=sqrt((2xx16)/g)=4sqrt(2/g)`
Time interval between two drops is
`t_"interval"=(1/(n-1))t=(1/4)t=sqrt(2/g)`
where n= number of drops .
Step-ii :
Distance between first and second drops
`=S_1-S_2=1/2 g t_"interval"^2[4^2-3^2]=7m`
Distance between second and third drops
`=S_2-S_3=1/2 "gt"_"interval"^2[3^2-2^2]=5m`
Distance between third and fourth drops
`=S_3-S_4=1/2 "gt"_"interval"^2[2^2-1^2]=3m`
Distance between fourth and fifth drops
`=S_4-S_5=1/2"gt"_"interval"^2[1^2-0]`=1m