12. A stone is dropped from the top of tower of height h. After 1
second another stone is dropped from the balcony 20 m belowthe top. Both reach the bottom simultaneously. What is the value
of h? (Take g = 10 ms-2)
a)3125 m
b) 312.5 m
c) 31.25 m
d) 25.31 m

Let t seconds be the time taken for the first stone to reach the ground.

Using s = ut + 0.5at^2, with s = H, u = 0, a = 10:

H = 0.5 x 10 x t^2

H = 5t^2

The time taken for the second stone to reach the ground will be (t - 1) seconds. The stone will fall from a height of H - 20 metres.

Use s = ut + 0.5at^2, with s = H - 20, u = 0, a = 10, t = (t - 1):

H - 20 = 0.5 x 10 (t - 1)^2

H - 20 = 5(t - 1)^2

We know that H = 5t^2:

5t^2 - 20 = 5(t - 1)^2

5t^2 - 20 = 5(t^2 - 2t +1)

5t^2 - 20 = 5t^2 - 10t + 5

-20 = -10t +5

10t = 25

t = 2.5

Substituting for H:

H = 5 x 2.5^2 = 31.25 metres