Answer
$v_{min}=0.14m/s$
Work Step by Step
Call the time it takes for the ball to travel such a distance $\Delta t$; the minimum linear speed of the ball is $$v_{min}=\frac{d}{\Delta t} (1)$$
For the ball not to be hit, $\Delta t$ has to be smaller than the time it takes before the next blade arrives, which we need to calculate next.
The windmill has 8 blades and 8 openings of the same size, so we can treat it as 16 similar parts. Therefore, the angular displacement of an opening is $$\Delta\theta=\frac{2\pi}{16}=\frac{\pi}{8}rad$$
We have $\overline\omega=1.25rad/s$. So $$\Delta t=\frac{\Delta\theta}{\overline\omega}=0.314s$$
Plugging it back to (1), we find $v_{min}=0.14m/s$
