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 detaches from the roaf. Find the distance between the successive drops.

Drops of water fall at regular intervals from the roof of a building o

1.	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 detaches from the roaf. Find the distance between the successive drops.
Answer» Solution :Step -I : Time taken by the first drop to touch the ground `=t=sqrt((2h)/g) ` For h=16m, `t=sqrt((2 XX 16)/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 gt_("interval")^(2) [4^(2)-3^(2)]=7M` Distance between second and third drops `=S_(2)-S_(3)=1/2 "gt"_("internal")^(2) [3^(2)-2^(2)]=5m` Distance between third and fourth drops `=S_(3)-S_(4)=1/2 "gt"_("internal")^(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`.