posted by Jackie .
A rocket is fired vertically with an upward acceleration of 30 m/s2. After 20 s, the engine shuts off and the rocket then continues rising (while in free-fall). The rocket eventually stops rising and then falls back to the ground.
(a) What is the highest point the rocket reaches?
(b) What is the total time the rocket is in the air?
(c) What is the speed of the rocket just before it hits the ground?
Start by computing the velocity and altitude achieved while the engine is on. Then write the equation for height and velocity during free fall. It's not that hard.
When the velocity is zero during the free fall stage, maximum height has been reached. Solve for that time, and the altitude reached then. So much for (a). For (b), solve for the time when the altitude is zero.
For (c), a shortcut would be to take the kinetic energy and altitude H at burnout, add 2gH to V^2 at burnout, and solve for the new V^2 at impact
Show us your work if you need further assistance here.