Answer
$$t=5.12 \ seconds$$
Work Step by Step
The stone hits the water at the time where the height is 0 and $t>0$. Thus, we find:
$$ 0=-16t^2+ 32t + 256 $$
Applying the quadratic formula:
$$ t_{1,2}=\frac{-b\pm \sqrt{b^2-4ac}}{2a} \\ t_{1,\:2}=\frac{-32\pm \sqrt{32^2-4(-16)256}}{2(-16)} \\ t=1\pm \sqrt{17} $$
Since $t$ must be positive:
$$ t=1+\sqrt{17} \\ t=5.12 \ seconds$$
