The projectile has a height <em>h</em> at time <em>t</em> given by
<em>h</em> = (14.0 m/s) <em>t</em> - 1/2 <em>g t</em> ²
where <em>g</em> = 9.80 m/s² is the magnitude of the acceleration due to gravity. Solve for <em>t</em> when <em>h</em> = 0 :
0 = (14.0 m/s) <em>t</em> - 1/2 <em>g t</em> ²
0 = 1/2 <em>t</em> (28.0 m/s - <em>g t</em> )
1/2 <em>t</em> = 0 <u>or</u> 28.0 m/s - <em>g</em> <em>t</em> = 0
The first equation says <em>t</em> = 0, which refers to the moment the gun is first fired, so we ignore that solution. We're left with
28.0 m/s - <em>g t</em> = 0
<em>t</em> = (28.0 m/s) / <em>g</em>
<em>t</em> = (28.0 m/s) / (9.80 m/s²)
<em>t</em> ≈ 2.86 s
