Answer
(a) $20\ sec$.
(b) between 2 sec and 18 sec.
Work Step by Step
(a) Given $s=-16t^2+320t$, to hit the ground, we need $s=0$ or $-16t^2+320t=0$ which gives $t=0, 20$. Discard $t=0$ as it is the starting point, thus $t=20\ sec$.
(b) Let $s\gt 576$, we have $-16t^2+320t\gt576$ or $16t^2-320t+576\lt0$. Factor to get $16(t-2)(t-18)\lt0$ and the boundary points are $t=2,18$. Use test values $t=0, 3, 19$ for intervals $(0,2),(2,18),(18,20)$ on the inequality and get $False,True,False$. Thus the answer is the middle interval $(2,18)$ that is between 2 sec and 18 sec.
