$3.$ Consider an air$-$breathing jet engine which is flying at a velocity of $600$ feet per second. For every $\backslash (\backslash$mathrm$\{$lbm$\}/\backslash$mathrm$\{$second$\}\backslash )$ of air mass flow, a $\backslash (0\mathrm{.}030\backslash$mathrm$\{$lbm$\}/\backslash$mathrm$\{$sec$\}\backslash )$ mass flow of fuel is injected into the engine. The thrust force is $5000$ lbf$.$ ; the entrance pressure equals the ambient pressure at the altitude $(0\mathrm{.}5$ atm $)$ and the exhaust pressure is $0\mathrm{.}75$ times the ambient atmospheric pressure. The incoming air temperature is $\backslash (525^\{\backslash$circ$\}\backslash$mathrm$\{$R$\}\backslash ).$ The entrance area and exhaust areas are both ten square feet. Determine:

$($a$)$ exhaust velocity

$($b$)$ specific fuel consumption