consider the motion of the coin in vertical direction :
Assuming down direction as positive and top of building as origin
Y₀ = initial position of displacement of the coin at the top of building = 0 m
Y = final position of displacement of the coin as it hits the ground = h
t = time taken to hit the ground
a = acceleration = acceleration due to gravity = g
v₀ = initial velocity at the top of the building = 0 m/s
using the equation
Y = Y₀ + v₀ t + (0.5) a t²
h = 0 + 0 t + (0.5) g t²
h = (0.5) g t² eq-1
consider the motion of the coin for time "t/2"
Y₀ = initial position of displacement of the coin at the top of building = 0 m
Y' = final position of the coin after time "t/2"
t' = time of travel = t/2
a = acceleration = acceleration due to gravity = g
v₀ = initial velocity at the top of the building = 0 m/s
using the equation
Y' = Y₀ + v₀ t' + (0.5) a t'²
Y' = 0 + 0 t + (0.5) g (t/2)²
Y' = (0.5) gt²/4
using eq-1
Y' = h/4 since h = (0.5) g t²
