\(s = vt -0.5gt^2\)
\(2s =2vt -gt^2\)
\( gt^2 -2vt = -2s \)
\(t^2 - \frac{2v}{g}t = \frac{-2s}{g} \)
\(t^2 -\frac{2v}{g}t + (\frac{v}{g})^2 = \frac{-2s}{g} + (\frac{v}{g})^2\)
\( (t-\frac{v}{g})^2 = \frac{v^2 - 2sg}{g^2}\)
\(t - \frac{v}{g} = \frac{\sqrt{v^2-2sg}}{g}\)
\(t = \frac{v\pm\sqrt{v^2-2sg}}{g}\)
(b)When \(s = 450\)
\(t = \frac{300 + \sqrt{300^2-2(450)(32)}}{32}\)
\(t = 17.11 \text{sec}\)
\(t = \frac{300 - \sqrt{300^2-2(450)(32)}}{32}\)
\(t = 1.64 \text{sec}\)
When \(s = 0\)
\(t = \frac{300 + \sqrt{300^2-2(0)(32)}}{32}\)
\(t = 18.75 \text{sec}\)
\(t = \frac{300 - \sqrt{300^2-2(0)(32)}}{32}\)
\(t = 0 \text{sec}\)