$1.$ Supersonic Wedge:

Consider the $2$D wedge shown in the figure. The wedge has a nose angle of $\backslash (10^\{\backslash$circ$\}\backslash )$ and is inclined $\backslash (8^\{\backslash$circ$\}\backslash )$ relative to a flow at Mach $2\mathrm{.}0,$ which has a stagnation pressure of $2$ bar.

$($a$)$ Draw the wedge with the appropriate waves at the nose.

$($b$)$ Determine the Mach number, static pressure, and static temperature above the wedge.

$($c$)$ Determine the Mach number, static pressure, static temperature, and stagnation pressure below the wedge.

$($d$)$ At approximately what inclination angle would a detached bow shock form in front of the wedge?