There are three stones, A, B, and C, which are all projected from the same point with the same initial velocity. Stone A is projected vertically upwards, stone B is projected vertically downwards, and stone C is simply dropped from the same point. It takes stone A, 1 second and stone B, 4 seconds to reach the ground. What is the time taken for stone C to reach the ground?

We can consider height of the tower as H m

First stone is projected vertically with velocity v m/s

s=ut+(1/2)at²

H = -v x u + (1/2)g x 4²

    = -uv + 8g    .......................(1)

2nd stone is projected vertically with velocity v m/s and it reaches the ground in 1s.

H = v + (1/2)g .......................(2)

From eq (1) and (2)

-uv + 8g= v+(1/2)g

5v = 8g -(1/2)g

v = (3/2)g

Then the height of tower

H = (3/2)g x 1 + (1/2)g x1²

    = 2g