A rocket is fired straight up from the ground. It contains a payload and two stages of solid rocket fuel that are designed to burn for $10\mathrm{.}0s$ and $5\mathrm{.}00s,$ respectively, with no time interval between them. In stage $1$ the upward acceleration is $15\mathrm{.}0\frac{m}{s^2}.$ In stage $2$ the acceleration is $12\mathrm{.}0\frac{m}{s^2}.$ Neglecting air resistance, $($a$)$ how fast is the payload moving at the end of stage $1?($b$)$ How fast is it moving at the end of stage $2?($c$)$ What is the altitude of the rocket at the end of stage $1?($d$)$ What is the altitude of the rocket at the end of stage $2?($e$)$ What is the maximum altitude obtained by the payload? $($f$)$ What is the total travel time of the payload from launch to landing? Assume the acceleration due to gravity is constant. Example $2-6$