A test rocket is fired vertically upward from a well. A catapult gives it an initial speed of 81.0 m/s at ground level. Its engines then fire and it accelerates upward at 4.10 m/s2 until it reaches an altitude of 940 m. At that point its engines fail, and the rocket goes into free fall, with an acceleration of -9.80 m/s2. (You will need to consider the motion while the engine is operating separate from the free-fall motion.)
(a) How long is the rocket in motion above the ground?
(b) What is its maximum altitude?
(c) What is its velocity just before it collides with the Earth?