Answer
$104.5\ ft/sec$
Work Step by Step
Step 1. Given the model equation $D = 0.1s^2 - 3s + 22$ and $D=800\ ft$, we have $0.1s^2 - 3s + 22=800\longrightarrow 0.1s^2 - 3s -778=0$
Step 2. We can identify $a=0.1, b=-3, c=-788$, thus $s=\frac{3\pm\sqrt {(-3)^2-4(0.1)(-778)}}{2(0.1)}=\frac{3\pm\sqrt {320.2}}{0.2}$
Step 3. As the speed need to be positive, choose the $+$ sign, we have $s=\frac{3+\sqrt {320.2}}{0.2}\approx104.5\ ft/sec$
