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A catapult launches a test rocket vertically upward from a well, giving the rocket an initial speed of 80.0 m/s at ground level. The engines then fire, and the rocket accelerates upward at 5.00 m/s^2 until it reaches an altitude at 1000m. At that point, its engines fail and the rocket goes into free fall, with an acceleration of -9.80 m/s^2. (a) For what time intervals is the rocket in motion above the ground? (b) what is its maximum altitude?

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