Problem $2$: $(30$ points total$)$

A thin symmetric airfoil has chord length $c$ and a thickness distribution

$\frac{h(x)}{c}=0\mathrm{.}3[\frac{x}{c}-(\frac{x}{c}{)}^2]$

It is placed at zero angle of attack in a freestream with Mach number $M_1=2.$

Determine the drag coefficient $C_d.$