Drops of water fall at regular intervals from the rood of a building of height H=16m,the first drop striking the ground at the same moment as the fifth drop detaches from the rood.Find the distance between the 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_(int erval)=(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)"gt"_("int erval")^(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`.