Question

4 One drops a penny from the top of the
Empire State building on to the ground
below. The height of the Empire State
building is 443 m.
How long will it take for the penny to
strike the ground, assuming no air
resistance?

Answer 1

Answer:

The penny will take 9.504 seconds to strike the ground if air resistance is neglected.

Explanation:

The penny experiments a free fall, which is uniform accelerated motion due to  Earth's gravity. This kind of motion neglects the effects of air resistence and the rotation of the planet. In this time we must calculate the time taken by the penny to hit the ground from top of the Empire State Building from the following equation of motion:

$y = y_{o}+v_{o}\cdot t + \frac{1}{2}\cdot g\cdot t^{2}$ (Eq. 1)

Where:

$y_{o}$ - Initial position of the penny, measured in meters.

$y$ - Final position of the penny, measured in meters.

$v_{o}$ - Initial velocity of the penny, measured in meters per second.

$g$ - Gravitational acceleration, measured in meters per square second.

$t$ - Time, measured in seconds.

If we know that $y_{o} = 443\,m$, $y = 0\,m$, $v_{o} = 0\,\frac{m}{s}$ and $g = -9.807\,\frac{m}{s^{2}}$, we obtain this quadratic function:

$4.904\cdot t^{2} -443 = 0$

All roots can be found easily by factorizing the polynomial:

$4.904\cdot (t^{2} - 90.335) = 0$

$4.904\cdot (t-9.504)\cdot (t+9.504) = 0$

The first binomial offer to us the only answer that is physically reasonable:

$t = 9.504\,s$

The penny will take 9.504 seconds to strike the ground if air resistance is neglected.