## Answer: Difficult to calculate, but under 8.81 seconds.

Calculating how long it takes an object to fall a certain
distance is a difficult question if you want an exact answer, but
if you're willing to look at a simplified model (ignoring factors
such as air resistance/frictions, which would be considerable), a
crude approximation can be reached.

The acceleration due to gravity of an object is 9.81 m/s2
*(meters per second per second)* down. The amount of
displacement resulting from a given acceleration over time is
.5a*t*2, where *t* is the amount of time (in seconds).
The amount of displacement we need to equal is the height of the
roof of the Empire State Building, 381 m *(1250 ft)*.

After substituting our values into the displacement/acceleration
equation, giving us -381 = .5(-9.81)*t*2. We can find our
amount of time by isolating *t*. Doing this give us our final
result of **8.81** seconds. If we assume that non-gravity
factors would not be accelerating your decent, we can treat this as
an upper limit to the result in real life. if you try you cant go
past the bars

How ever if you decide to use feet units you come up with 6.154
seconds. Acceleration due to gravity is approximately -32.174 feet
per second2. The Empire State building is 1250 feet tall. So the
height, Y, at time, t, 0 is 1250.

The acceleration equation of the scenario would at first
Y"=-32.174t. When we integrate this to find the velocity equation
we recieve: Y'=-16.087t2+C. The integrating constant, C, would
represent a starting velocity. Since the person "fell" off the
building the initial velocity is 0, so Y'=-16.087t2. In order to
find the position equation we integrate once more, yielding:
Y=-5.36233t3+C. The integrating constant, C, in this case
represents initial position which we know is 1250. So the position
equation is: Y=-5.36233t3+1250. To find out when he hits the ground
we solve for when height, Y, equals 0. 0=-5.36233t3+1250. This
yields a time value of 6.1544 seconds.

*Note: This answer also ignores air resistance.