$(25$ points$)$ Consider the airfoil obtained using the Joukowsky transformation and a generating circle of radius $"$a$"$ and centered at $(-\mathrm{.}04,\mathrm{.}02).$ Take the free$-$stream velocity to be unity and ${}_T$ equal to $(1,0).$

a$.$ At an angle of attack of $10$ degrees, what is the magnitude of the velocity on the upper surface of the airfoil at the chordwise location corresponding to the point on the circle given by $=3\frac{}{4}?$

b$.$ What is the value of $qt\frac{e^{-}}{U_{}}($trailing$-$edge velocity ratio$)$ for this airfoil at the given operating condition?

c$.$ If it is assumed that $c=4a,$ what is the sectional lift coefficient at the given operating condition?