Question

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?

Answer 1

Answer:

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

Answer 2

The height h of the building is 9.8 m.

The given parameter:

• initial velocity of the  Green Lantern, u = 0

• time of half-fall of the motion, t = 1.0 s

To find:

• the height h of the building

To find the height h of the building, we first find the half of the distance traveled;

$s = ut + \frac{1}{2} gt^2\\\\s = t(0) + 0.5 \times 9.8 \times 1^2\\\\s = 4.9 \ m$

The height of the building = 2 of the distance of fall

height, h = 2 x 4.9 m

height, h = 9.8 m

Thus, the height h of the building is 9.8 m.

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