Problem $3$: $(40$ points total$)$

Consider a thin, symmetric airfoil with a $1-m$ chord in an airstream with a velocity of $100\frac{m}{s}$ at standard sea level conditions.

$($a$)$ List the assumptions of thin airfoil theory.

$($b$)$ Describe the concept of the Kutta condition. Starting from the fundamental equation of thin airfoil theory, demonstrate how the Kutta condition is satisfied for this airfoil.

$($c$)$ If the lift per unit span is $1343\frac{N}{m},$ calculate the lift coefficient and determine the angle of attack.

$($d$)$ Calculate the moment coefficients about the quarter$-$chord point, and about the trailing edge.