Problem $1.-$ For an airfoil with the given mean camber line of a chord length of $C_w=1m$ as follows:

$Z(x)=0\mathrm{.}15[\frac{x}{2}-\frac{x^2}{c_w^2}-\frac{3}{c_w}]$

Using thin airfoil theory, calculate

a$)C_{m,\frac{c}{4}}$ for the airfoil above

b$)$ The increment $C_m,\frac{c}{4}$ due to the flap with a deflection angle of $30$ and a chord length of $C_f=0\mathrm{.}25C_w.$

c$)$ The total moment coefficient of the integrated wing$-$flap configuration