Consider a Mach $2\mathrm{.}5$ flow. It is desired to slow this flow to a subsonic speed. Consider two separate ways of achieving this: $(1)$ the Mach $2\mathrm{.}5$ flow is slowed by passing directly through a normal shock wave; $(2)$ the Mach $2\mathrm{.}5$ flow first passes through an oblique shock with a $\backslash (40^\{\backslash$circ$\}\backslash )$ wave angle, and then subsequently through a normal shock. These two cases are sketched in the Figure below.

a$)$ Calculate the ratio of the final total pressure values for the two cases, that is$,$ the total pressure behind the normal shock for case $2$ divided by the total pressure behind the normal shock for case $1.(\backslash (15\backslash \%\backslash ))$

b$)$ Comment on the significance of the result. $(\backslash (10\backslash \%\backslash ))$

c$)$ Explain why modern supersonic aircraft have oblique shock inlet. $(5\backslash \%)$