Problem $4.(20$pts$)$ Consider a wing$-$body model with $C_{m_{ac,wb}}=-0\mathrm{.}022,{\stackrel{}{x}}_{cg}=0\mathrm{.}33,{\stackrel{}{x}}_{ac,wb}=$

$0\mathrm{.}22,a_{wb}=0\mathrm{.}08.$ The area and chord of the wing are $0\mathrm{.}1m^2$ and $0\mathrm{.}1$ m $,$ respectively. Now

assume that a horizontal tail is added to this model. We have the flowing parameters: $l_t=0\mathrm{.}17m,$

$S_t=0\mathrm{.}02m^2,i_t=2\mathrm{.}5,a_t=0\mathrm{.}1$ per degree, ${}_0=0$ and del$\frac{}{d}el=0\mathrm{.}4.$

X$\_$NP $/$ c $=0\mathrm{.}3217,$ For alpha $=9\mathrm{.}38$ deg Gmacg $=-0\mathrm{.}0458$

Obtain the linearized y$-$force equation using the above trim condition. Show your work and clearly

write down the result. Are the longitudinal and lateral linearized dynamics of the airplane in this

case decoupled?