A simple but effective anemometer to measure wind speed can be made from a thin plate hinged to deflect in the wind. Consider a thin plate made from brass that is \(20 \mathrm{~mm}\) high and \(10 \mathrm{~mm}\) wide. Derive a relationship for wind speed as a function of deflection angle, \(\theta\). What thickness of brass should be used to give \(\theta=30^{\circ}\) at \(10 \mathrm{~m} / \mathrm{s}\) ?