$7\mathrm{.}10$ Consider the solid rocket motor shown in Figure $7\mathrm{.}28.$ During a test firing of this motor, the initial $($just after ignition$)$ and final $($just prior to burnont$)$ chamber pressures were $3$ and $7\mathrm{.}5$ MPa $,$ respectively. The propellant used in this test has a density of $1800k\frac{g}{m^3}$ and a characteristic velocity of $1500\frac{m}{s}.$ Assuming the propellant burns according to St$.$ Robert's law