Problem $4$: turbojet engine $(\backslash (\backslash$mathbf$\{30\}\backslash$mathbf$\{$~ p t s$\}\backslash )).$ Consider a turbojet mounted on a stationary test stand at sea level. The inlet and exit areas are the same, both equal to $\backslash (0\mathrm{.}45\backslash$mathrm$\{$~m$\}^\{2\}\backslash ).$ The velocity, pressure, and temperature of the exhaust gas are $\backslash (400\backslash$mathrm$\{$~m$\}/\backslash$mathrm$\{$s$\},1\mathrm{.}0\backslash$mathrm$\{$~atm$\}\backslash ),$ and $750$ K $,$ respectively.

$($a$)(20$ pts$)$ Calculate the static thrust of the engine.

$($b$)(10$ pts$)$ Calculate the propulsive efficiency under the conditions.

$($Note: Static thrust of a engine is the thrust produced when the engine has no forward motion. Even though the engine is stationary, it is sucking air into the inlet at a nonzero flow velocity.$)$