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?