Answer
(a) $s(t)=-16t^2+64t+200$
(b) from 0.78 to 3.22 seconds.
Work Step by Step
(a) Given $s_0=200\ ft, v_0=64\ ft$, we have $s(t)=-16t^2+64t+200$ which describe the height of the ball as shown in the graph.
(b) Let $s(t)\gt 240$, we have $-16t^2+64t+200\gt 240$. Graph the line $y=240$, we can find two intersect points at $t=0.78\ sec$ and $t=3.22\ sec$. Thus, the height will be over 240 feet from 0.78 to 3.22 seconds.
