A small rocket motor, fueled with hydrogen and oxygen, is tested on a thrust stand at a simulated altitude of \(10 \mathrm{~km}\). The motor is operated at chamber stagnation conditions of \(1500 \mathrm{~K}\) and \(8.0 \mathrm{MPa}\) gage. The combustion product is water vapor, which may be treated as an ideal gas. Expansion occurs through a converging-diverging nozzle with design Mach number of 3.5 and exit area of \(700 \mathrm{~mm}^{2}\). Evaluate the pressure at the nozzle exit plane. Calculate the mass flow rate of exhaust gas. Determine the force exerted by the rocket motor on the thrust stand.