A test rocket is fired vertically in the air from a well. A catapult provides it an initial speed of 81.0 m/s at ground level. Its engines then fire and it accelerate upward at 3.90 m/s^2 till it arrive at an altitude of 930 m. At that point its engines fail, and the rocket goes into free fall, with an acceleration of -9.80 m/s^2. (You will require considering the motion while the engine is operating separate from the free-fall motion.)
i) Determine how long is the rocket in motion above the ground?
ii) Determine the maximum altitude?
iii) Determine its velocity just prior to it collides with the Earth?