An external$-$compression supersonic inlet with a single ramp operates in critical mode as shown. The flight speed is $750\frac{m}{sec}$ where the ambient air $($static$)$ temperature and pressure are $224$ K and $20$ kPa respectively.

Neglect all losses except those occurring due to shocks. Also, use $=1\mathrm{.}4$ and $R_{\text{a}\text{i}\text{r}}=287\frac{m^2}{s^2(K)}$ for this problem.

$($a$)$ Calculate inlet total pressure recovery due to shocks. In other words, what is the stagnation pressure ratio, $\frac{p_{02}}{p_{000}}=?($show or explain your work$)$

$($b$)$ Estimate the inlet adiabatic efficiency for this case. In other words, what is ${}_d=?$