Drope of water fall at regular intervals from the roof of a building of height `H=16m`, the first dro striking the ground at the same moment as the fifth drop detaches from the roof. Find the distance between the successive drops.

Explanation

Step-I : Time taken by the first • 5
drop to touch the ground = `t=sqrt((2h)/(g))` • 4
For `h=16m,t=sqrt((2xx16)/(g))=4sqrt((2)/(g))` • 3
Time interval between two drops is • 2
`t_("interval")=((1)/(n-1))t=((1)/(4))t=sqrt((2)/(g))` • 1
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)g t_("interval")^(2)[3^(2)-2^(2)]=5m`
Distance between third and fourth drops
`=S_(3)-S_(4)=(1)/(2)g t_("interval")^(2)[2^(2)-1^(2)]=3m`
Distance between fourth and fifth drops.
`=S_(4)-S_(5)=(1)/(2)g t_("interval")^(2)[1^(2)-0]=1m`.