$($Show work and steps. Circle$/$box final answers$)$Problem $1$

The pressure measured by a Pitot tube located downstream of a normal Shock is $3$ atm and the

total$-$ to$-$static temperature ratio downstream of the shock is $\frac{T_{0_2}}{T_2}=1\mathrm{.}098.$ Calculate :

a$)$ The static pressure downstream of the shock

b$)$ The Mach number upstream of the shock

c$)$ The static pressure upstream of the shock

d$)$ The entropy change across the shock

$($You may use $C_p=1\mathrm{.}005k\frac{J}{kg*K},C_v=0\mathrm{.}718k\frac{J}{kg*K},R=287\frac{J}{kg*K},$ and $=1\mathrm{.}4)$