How long will it take for the penny to hit the ground if the building is 1,101 feet tall?

Question

You are standing on top of a building, and you drop a penny from the highest point.  How long will it take for the penny to hit the ground if the building is 1,101 feet tall?

Remember that gravitational acceleration is 32 ft/s2. Please report your answer in seconds.  Assume that there is no air resistance.

Answer 1

One of the kinematic equations of motion is x_f = 1/2at² + v_it + x_i but if you consider that you can set up your coordinate plane at the top of the building meaning x_i (initial "x") is zero. And since you are dropping the coin, the initial velocity (v_i) is zero as well therefore the equation simplifies to x = 1/2at²

Plug in a = 32 ft/s² and x = 1101 feet and get:

1101 = 32t²

t² = 1101/32

t² = 34.40625

t = √34.40625

t = 5.9 seconds