$12\mathrm{.}6$

A $0\mathrm{.}5$ ounce model rocket is launched vertically from rest at time $\backslash ($ t $\backslash )\backslash (=0\backslash )$ seconds with a thrust of $0\mathrm{.}9$ lb for $0\mathrm{.}3$ seconds and no thrust for $\backslash ($ t$>0\mathrm{.}3\backslash$mathrm$\{$~s$\}\backslash ).$ Neglecting air resistance and the decrease in mass of the rocket, determine $($a$)$ the maximum height h reached by the rocket, $($b$)$ the time required to reach this maximum height. Provide simple free$-$body diagrams and kinetic diagrams for the rocket in it's two conditions $($thrust and no$-$thrust$).$