Answer
$(0,3)$; between 0 and 3 seconds.
Work Step by Step
Step 1. The rooftop is 160 feet high. For the ball to be above the rooftop, we have $s(t)\gt160$
Step 2. With the given function, we have
$-16t^2+v_0t+s_0\gt160$
Step 3. The initial conditions are $v_0=48\ ft/sec$ and $s_0=160\ ft$. We have $-16t^2+48t+160\gt160$, which gives $16t^2-48t\lt0$
Step 4. Factoring the left side, we have $16t(t-3)\lt0$ and the boundary points are $t=0, 3$
Step 5. With $t\geq0$, use the test points to examine signs of the left side across the boundary points. We have
$(0)...(-)...(3)...(+)...$
Thus the solutions are $(0,3)$ -- that is, between 0 and 3 seconds.
