The rocket used to launch the $540-$kg spacecraft of Prob. $14\mathrm{.}95$ is rede signed to include two stages A and B$,$ each of mass $9\mathrm{.}5$ Mg$,$ including $8\mathrm{.}9$ Mg of fuel. The fuel is again consumed at a rate of $225$ kg$/$s and ejected with a relative velocity of $3600$ m$/$s$.$ Knowing that when stage A expels its last particle of fuel, its casing is released and jettisoned, determine $($a$)$ the speed of the rocket at that instant, $($b$)$ the maximum speed imparted to the spacecraft.