A new type of space vehicle is sent vertically upward, from the ground, with an initial speed of 80.0 m/s. The engines then fire, and the rocket accelerates up-ward at

4.00 m/s?until it reaches an altitude of 1 000 m. At that point, its engines fail and the rocket goes into free fall, with an acceleration of -9.80 m/s?. (a) For what time interval is the rocket in motion above the ground? (b) What is its maximum altitude? (c) What is its velocity just before it hits the ground?