$19-$ For the wing$-$tail configuration below. The wing span is $14$ m and chord length is $2$ m $.$ The wing has a lift coefficient given by the relation:

$C_{L_w}=0\mathrm{.}4+0\mathrm{.}15{}_w$

The Tail has a span of $5$ m and chord length of $0\mathrm{.}7$ m with a symmetric airfoil and lift curve slope of $0\mathrm{.}1de{g}^{-1}.$

The distance between the tail aerodynamic center and the center of gravity is $4$ m while that of the wing is $1\mathrm{.}0$ m $.$

Given that the wing and tail incidence angles are zero. Assume that the down$-$ vash angle is zero and that the dynamic pressure of the tail is equal to the dynamic pressure of tl e wing

Evaluate:

$($a$)$ if the airplane is flying at an angle of attack of zero at sea$-$lev ${?}_l$ conditions with a speed of $100\frac{m}{s}.$ What is the total lift generated by the confi ; uration $($wing and tail combined$)[5$ points$]$

$($b$)$ If the wing has a moment coefficient of $(-0\mathrm{.}1),$ evaluate the moment around the center of gravity if the airplane is flying at an angle of attack equal to zero and at a speed of $100\frac{m}{s}[5$ points$]$

$($c$)$ Starting with an expression for the total moment of the airplane, write down an expression for the moment coefficient of the airplane $[5$ points$]$