Answer
$4\ m/s$
Work Step by Step
Given:
Radius of each spoke $r=30\ cm = 0.3\ m$
Angular velocity of the wheel $\omega = 2.5\ rev/s$
Length of the arrow $L =20\ cm = 0.2\ m$
Formula for the angular velocity is $\omega = \frac{\Delta\theta}{\Delta t}$
(where $\Delta\theta$ is the number of revolutions made)
Also, the time takes for $\frac{1}{8}$ revolution is:
$\Delta t = \frac{\Delta\theta}{\omega}$
$\Delta t = \frac{(\frac{1}{8})\ rev}{2.5\ rev/s}$
$\Delta t = 0.05\ s$
The minimum speed of the arrow is $v=\frac{L}{\Delta t}$. Therefore;
$v=\frac{0.2\ m}{0.05\ s}$
$v=4\ m/s$
