Acatapult launches a test rocket vertically upward from a well, giving the rocket an initial speed of 80.6 m/s at ground level. the engines then fire, and the rocket accelerates upward at 3.90 m/s2 until it reaches an altitude of 1040 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 and the free-fall motion separately.) (a) for what time interval is the rocket in motion above the ground?