Answer
(b) 154.3mi/h
(a) 7.071s
Work Step by Step
\[
\begin{array}{l}
s(t)=s_{0}+v_{0} t -\frac{g}{2} t^{2}\\
v(t)=v_{0}-g t
\end{array}
\]
$g=32 \mathrm{ft} / \mathrm{s}^{2}$
Using Formula (15) and Formula (16) from the book:
(a) $0=s(t)=800-16 t^{2}$
$\Rightarrow 7.071\mathrm{s}=\sqrt{\frac{-800}{-16}}=t$
$s_{0}=800$, $v_{0}=0$ and $s(t)=0$
(b) $-32 t=v(t)$
Velocity at $t=7.071$:
$v(50)= 7.071 \cdot (-32)=-226.27 \mathrm{ft} / \mathrm{s}=154.3 \mathrm{mi} / \mathrm{h}$
