$11$A$\mathrm{.}5.$ Velocity, temperature, and pressure changes in a shock wave. Air at $1$ atm and $70F$ is flowing at an upstream Mach number of $2$ across a stationary shock wave. Calculate the following quantities, assuming that $$ is constant at $1\mathrm{.}4$ and that hat$(C{)}_p=0\mathrm{.}24Bt\frac{u}{l}{b}_m*F$ :

$($a$)$ The initial velocity of the air.

$($b$)$ The velocity, temperature, and pressure downstream from the shock wave.

$($c$)$ The changes of internal and kinetic energy across the shock wave.

Answer: $($a$)2250f\frac{t}{s}$

$($b$)844f\frac{t}{s}$;$888R$;$4\mathrm{.}48$atm

$($c$)hat(U)=+61\mathrm{.}4Bt\frac{u}{l}{b}_m$;$hat(K)-86\mathrm{.}9Bt\frac{u}{l}{b}_m$