# A stone is falling from the top of a vertical tower. When it has fallen 'a' meter, another stone let dropped from a point 'x' meter below ..?

A stone is falling from the top of a vertical tower. When it has fallen 'a' meter, another stone is dropped from a point 'x' meter below the top. If they fall from rest and reach the ground together, find height of the tower.

### 2 Answers

- Pramod KumarLv 71 month ago
The first stone, after falling AB ( = a ) m has acquired a velocity of √(2 ag) and is at 'B' . The second stone now starts from rest from 'C' such that AC = x. and CB = (x - a). They reach together at D say in time (t) second. Then --

Distance covered by First stone from B to the ground (BD)----

BD = (h-a) = √(2 ag) * t + (1/2) g t² ...... (1)

For the second stone, distance covered (CD) = (h-x)

( h-x ) = 0 t + (1/2) g t² .................. (2)

from (2) : (1/2) gt² = ( h - x ).

Substitute this value in (1)----

(h-a) = √(2 ag) * t + ( h - x )

=> - a = √(2 ag) * t - x

=> t = ( x - a )/√(2 ag) =====>>> t² = (x-a)²/ 2 ag

Substitute this value in (2)

=> h - x = (1/2) g * [ (x-a)²/ 2 ag ]

........ (x-a)² + 4 a x ..... (x + a)²

=> h = ------------------ = --------------- .......... Answer

................ 4 a ........ ... .. 4 a