$1)$ The Piper Cherokee $($a light, single$-$engine general aviation aircraft$)$ has a wing area of $15\mathrm{.}82$ and a wingspan

of $9\mathrm{.}75$ m$.$ Its maximum gross mass is $1111\mathrm{.}3$ kg$.$ The wing uses an NACA $65-415$ airfoil, which has a lift slope

of $0\mathrm{.}1033/$deg and $=0=3.$ Assume $=0\mathrm{.}12.$ If the airplane is cursing at $193\mathrm{.}13$ km$/$h at standard sea level

at its maximum gross mass and is in straight$-$and$-$level flight, calculate the geometric angle of attack of the wing