Q$1(20$p$)$Consider a vertical axis drag based turbine as in the slides $2-8,$ with $R=20m,A=2m^2,$ and wind $V=8\frac{m}{s},=1\mathrm{.}2k\frac{g}{m^3}.$ Calculate the maximum angular speed, ${}_{\text{m}\text{a}\text{x}},$ by solving the equation

Power $=[C_{D_1}(V-R{)}^2-C_{D_2}(V+R{)}^2]\frac{}{2}AR=0($note that the equation is easily reduced to a quadratic equation in omega, with two solutions, of which just one solution is physical; explain why the other solution is not acceptable$).$

Calculate and plot the power produced by this turbine for $=0$cdots${}_{\text{m}\text{a}\text{x}}($take minimum $10$ values for $)$

Indicate the angular velocity for which

Power $=$ maximum