Answer
5.12 seconds
Work Step by Step
$s(t)=-16t^2+32t+256$
Height = $0 = s(t)$
$0=-16t^2+32t+256$
$0/-16=(-16t^2+32t+256)/-16$
$0=t^2-2t-16$
$a=1$, $b=-2$, $c=-16$
$x=(-b±\sqrt {b^2-4ac})/2a$
$x=(-(-2)±\sqrt {(-2)^2-4*1*-16})/2*1$
$x=(2±\sqrt {4+64})/2$
$x=(2±\sqrt {68})/2$
$x=(2±8.246)/2$
$x=(2+8.246)/2$
$x=10.246/2$
$x=5.123$
$x=5.12$
$x=(2-8.246)/2$
$x=-6.246/2$
$x=-3.123$
This answer is not valid since we are dealing with time. We can’t have a negative time, so this answer is not valid.
5.12 seconds
