Consider a rocket nozzle with exit conditions, $A_e=0\mathrm{.}1m^2,$ pressure $=50$kPa, and temperature $=1000K.$ The ambient pressure is $10$ kPa and the gas has a molecular weight and specific heat ratio of $18k\frac{g}{k}g-$mol and $1\mathrm{.}25,$ respectively. The axial flow velocity of the gas is $1,800\frac{m}{s}.$ Calculate the thrust. If the gas were to expand further, using a nozzle extension to a point where the exit pressure matches the ambient pressure, what would the thrust be$?$ If the gas is not expanded further in a nozzle but allowed to expand outside the nozzle to a point where the pressure matches the ambient, sketch the velocity field in the envelope outside the nozzle along which the pressure of the stream approximately matches the pressure of the ambient air. How much off$-$axis linear momentum is created in this plume?