Answer
$60\ \ \mathrm{f}\mathrm{t}/\mathrm{s}$
Work Step by Step
Solving exercise 70, we found that
$v(t)=-32t+v_{0} \quad$ and $s(t)=-16t^{2}+v_{0}t+h_{0},$
where $h_{0}$ is the initial height. We can take it to be $0$.
We want the time it takes for the chalk to strike the ceiling when $v_{0}=100$
$100= -16t^{2}+100t$
$16t^{2}-100t+100=0\quad/\div 4$
$4t^{2}-25t+25=0\qquad\left[\begin{array}{ll}
t& =\dfrac{25\pm\sqrt{625-4(4)(25)}}{2(4)}\\
& \\
& =\dfrac{25\pm 15}{8}\\
&
\end{array}\right]$
$t=\displaystyle \frac{10}{8}=\frac{5}{4}=1.25,\ \displaystyle \quad t=\frac{40}{8}=5$
We take $t=1.25$
(The other solution is the time it would take to pass the ceiling height, and fall back to it from above.)
Now, $v(t)=-32t+v_{0}=-32t+100,$
at time $t=1.25$
$v(1.25)=-40+100=60\ \ \mathrm{f}\mathrm{t}/\mathrm{s}$
