Gravity is quadratic.
<br>
Everything on Earth (buildings, airplanes, us) is struggling against its 
unrelenting downward pulling force.
<br>
Including anything you toss/shoot up.
<p>
<i>-16t<sup>2</sup></i> + <i>v<sub>0</sub>t</i> + <i>h<sub>0</sub></i>
<p>
height (in feet) of an object (ball, bullet, rock etc)
<br>
thrown/fired straight up with initial velocity <i>v<sub>0</sub></i>
(in feet per second)
<br>
from an initial height <i>h<sub>0</sub></i> (in feet) above the ground
<br>
<i>t</i> seconds after launch
<br>
(ignores air resistance!)
<p>
Examples:
<br>
<i>-16t<sup>2</sup></i> + <i>10t</i> + <i>50</i>
<br>
initial velocity: 10 ft/s  
&nbsp;&nbsp;&nbsp;&nbsp; starting height: 50 ft above ground
<br>
What is the object's height after t= 1, 2, 3 seconds?

<p>
<i>-16t<sup>2</sup></i> + <i>146t</i> 
<br>
initial velocity: 146 ft/s (about 100MPH) 
&nbsp;&nbsp;&nbsp;&nbsp; from ground (<i>h<sub>0</sub></i>=0)
<br>
What is the object's height after t= 1...10 seconds?
<p>
<i>-16t<sup>2</sup></i> +  <i>500</i>
<br>
initial velocity: 0 ft/s (<i>v<sub>0</sub></i>=0 i.e. dropped) 
&nbsp;&nbsp;&nbsp;&nbsp; 500 ft above ground
<br>
What is the object's height after t= 1...6 seconds?
<br>The <i>16t<sup>2</sup></i> means it speeds up by 16 ft/sec for each second of fall.
About 11 MPH. 
<br>
MPH*1.46 = ft/s
<br>
.68*ft/s = MPH 

<p>
Height is 0 when the object has landed.
<br>
<i>-16t<sup>2</sup></i> + <i>v<sub>0</sub>t</i> + <i>h<sub>0</sub></i> = 0
<br>
Solving this quadratic equation gives the value(s) of t when the object is on the ground. 

<p>
Metric version:
<br>
<i>-9.8t<sup>2</sup></i> + <i>v<sub>0</sub>t</i> + <i>h<sub>0</sub></i>