You have designed a rocket to be used to sample the local atmosphere for pollution. It is fired vertically with a constant upward acceleration of 18 m/s2. After 26 second, the engine shuts off and the rocket continues rising (in freefall) for a while. (Ignore any effects due to air resistance.) The rocket eventually stops rising and then falls back to the ground. You want to get a sample of air that is 20 kilometer above the ground.
(a) Determine the highest point your rocket reaches?
(b) Compute the total time the rocket is in the air.
(c) Determine the speed of the rocket just before it hits the ground.