The superhero Green Lantern steps from the top of a tall building. He falls freely from rest to the ground, falling half the total distance to the ground during the last 1.00 s of his fall.

What is the height h of the building?

57.18 m

Explanation:

Given:

- Distance traveled s (t_f) = 0.5*h

- Time in which the distance was traveled t_-t = 1.0 s

- Initial Velocity V_i = 0

- Initial distance from ground s (0) = h

Find:

Height of the building h

Solution:

Using Equation of motion of free fall from rest:

s (f) = s (0) + 0.5*g*t^2

Evaluate time taken to reach 0.5*h height of the building:

0.5*h = h - 0.5*9.81*t_1^2

t_1 = sqrt (h / g)

Evaluate time taken to reach bottom of the building:

0 = h - 0.5*9.81*t_2^2

t_2 = sqrt (2*h / g)

Hence,

t_2 - t_1 = 1

sqrt (h / g) - sqrt (2*h / g) = 1

Squaring both sides we get:

h/g + 2h/g - 2*sqrt (2) * h/g = 1

h (1+2-2sqrt (2)) = g

h = g / (3-2sqrt (2))

h = 57.18 m