Question

From a tap 10m high drops fall at regular intervals.When the first drop reaches the ground, the 5^th drop is about to leave the tap. Find the separation between 2^nd and 3^rd drop.

Answer 1

Height of tap = 10m and (g) = 10 m/sec2.
For the first drop
s=ut+(1/2)gt²
s=10 u=0
So 10=0+0.5*10*t²
10=5t²
So t=√2s
It means that the fifth drop leaves after one second of the first drop. Or, each drop leaves after every √2/2 sec
ie.if T is the time taken by first drop,the .T/2 by the second drop
ie.1/√2 sec
Distance covered by the secod. Drop in 1/√2 sec is
S=o+(1/2)*10*(1/√2)²
s=5*1/2
=2.5m


Now considering about third drop its time will be T/3
ie√2/3 sec
So its its dist is
S=0+(1/2)*10*(√2/3)²
S=5*4/3
S=20/3
S=6.67
So the separation is
6.67-2.50
=4.17m