Answer
a) 272 feet
b) 5.12 seconds
Work Step by Step
a)
The vertex of a parabola is at $x=-b/2a$.
$s(t)=-16t^2+32t+256$
$a=-16$, $b=32$, $c=256$
$x=-b/2a$
$x=-32/2*-16$
$x=-32/-32$
$x=1$
$t=1$
$s(t)=-16t^2+32t+256$
$s(1)=-16*1^2+32*1+256$
$s(1)=-16*1+32+256$
$s(1)=-16+32+256$
$s(1)= 272$
b)
$s(t)=-16t^2+32t+256$
height at water is 0 feet
$0=-16t^2+32t+256$
$x=(-b±\sqrt {b^2-4ac})/2a$
$x=(-32±\sqrt {32^2-4*-16*256})/2*-16$
$x=(-32±\sqrt {1024+64*256})/-32$
$x=(-32±\sqrt {1024+16384})/-32$
$x=(-32±\sqrt {17408})/-32$
$x=(-32±\sqrt {17*1024})/-32$
$x=(-32±32\sqrt {17})/-32$
$x=(1±\sqrt {17})$
$x=(1±4.123)$
$x=1+4.123$
$x=5.123$
$x=1-4.123$
$x=-3.123$ (this answer is ignored since we are looking for time, and we can't have a negative time)
