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 burnout$)$ chamber pressures were $3$ and $7\mathrm{.}5$ MPa, respectively. The propellant used in this test has a density of $1800$ kg$/$m $3$ and a characteristic velocity of $1500$ m$/$s$.$ Assuming the propellant burns according to St$.$ Robert$$s law $($rb $$ aP n c $),$ determine the burning rate coefficient $($a$)$ and exponent $($n$)$ Figure $7\mathrm{.}28$ Diagram for Problem $7\mathrm{.}10.$