Answer
$t=1.25$ seconds.
Work Step by Step
"Up" is the positive direction.
The starting point is at height $s(0)=100.$ We want the time it takes for $s(t)=0.$
The initial (downward) velocity is $v(0)=-60$.
$v(t)=-32t+v_{0}=-32t-60.$
and, $s(t)=\displaystyle \int v(t)dt$
$s(t)=\displaystyle \int(-32t-60)dt$
$=-16t^{2}-60t+C.$
Since $s(0)=100, $ it follows that $C=100,$
so
$s(t)=-16t^{2}-60t+100.$
We want the time it takes for $s(t)=0.$
$-16t^{2}-60t+100=0\qquad/\div(-4)$
$4t^{2}+15t-25=0$
$(4t-5)(t+5)=0$
$t=1.25$ or $t=-5$
Discarding the negative solution, $t=1.25$ seconds.
