A cyclist is able to attain a maximum speed of \(30 \mathrm{~km} / \mathrm{hr}\) on a calm day. The total mass of rider and bike is \(65 \mathrm{~kg}\). The rolling resistance of the tires is \(F_{R}=7.5 \mathrm{~N}\), and the drag coefficient and frontal area are \(C_{D}=1.2\) and \(A=0.25 \mathrm{~m}^{2}\). Determine the maximum speeds the bicyclist is actually able to attain with the \(10 \mathrm{~km} / \mathrm{hr}\) wind

(a) cycling into the wind,

(b) cycling with the wind. If the cyclist were to replace the tires with high-tech ones that had a rolling resistance of only \(3.5 \mathrm{~N}\), determine the maximum speed on a calm day, cycling into the wind, and cycling with the wind. If the cyclist in addition attaches an aerodynamic fairing that reduces the drag coefficient to \(C_{D}=0.9\), what will be the new maximum speeds?