Question

Suppose that there are N drops in the air, instead, with the first just reaching the bottom and the Nth just starting to fall. Say that the height of the fall is now h. Calculate the distance between the nth and (n+1)th drop (where n+1 ≤N)

Answer 1

When the Nth drop strted dropping, the first drop has already reached the ground. The time taken for the first drop to reach the ground can be calculated from the equation of motion,

(since the initial velocity is zero)

where,

Since all the drops are dropped periodically, the time interval between each drop will be,

(N-1, since we are counting from 1 to N)

ie, at the instance the first drop reaches the ground, the n'th drop will be at a height of,

Similarly for n+1'th drop.

The distance between n'th and n+1'th drop is,