Question

Drops of water from the roof of a house 6 m high fall at regular intervals. The first drop reaches the ground at an instant of time when third drop leaves the roof.Find the height of the second drop at that instant.

Answer 1

Time taken for the first drop to reach the ground will be

t = √(2h/g) [from s = ut + (1/2)at²]

or

t = √(2x6/10)

thus,

t = 1.095 secs.

Now, as the time interval between the first and second drop is equal to that of the second and the third drop (because drops dripping at regular intervals of time),

the time taken by the second drop will be

t' = t/2 = 0.5475 secs

So, the distance travelled by the second drop in that instant will be

s'= (1/2)gt²

or

s'= (1/2)x10x(0.5475)²

thus,

s' = 1.498 m