(a) Solve t in terms of s.

\(s = vt - 0.5gt^2\)

\(-\frac{-2s}{g} = \frac{-2vt}{g} + t^2\)

\(\frac{v^2}{g^2}-\frac{2s}{g} = t^2 - \frac{2vt}{g} + \frac{v^2}{g^2} \)

\(\frac{v^2 - 2sg}{g^2} = (t - \frac{v}{g})^2\)

\(\sqrt{\frac{v^2 - 2sg}{g^2}} = t- \frac{v}{g}\)

\(\frac{\sqrt{v^2-2sg}}{g} + \frac{v}{g}= t \)

\(\frac{v \pm \sqrt{v^2-2sg}}{g}= t \)

If \(v =300 \text{fps}\) solve \(t\) at \(s = 450\)

\(t = \frac{300 + \sqrt{300^2-2(450)(32)}}{32} \)

\(t = 17.11 \text{sec} \)

\(t = \frac{300 - \sqrt{300^2-2(450)(32)}}{32} \)

\(t = 1.64 \text{sec} \)

If \(v =300 \text{fps}\) solve \(t\) at \(s = 0\)

\(t = \frac{300 + \sqrt{300^2-2(0)(32)}}{32} \)

\(t = 18.75 \text{sec} \)

\(t = \frac{300 - \sqrt{300^2-2(0)(32)}}{32} \)

\(t = 0 \text{sec} \)