A catapult launches a test rocket vertically upward from a well, giving the rock

Question

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 4.00 m/s^2 until it reaches an altitude of 1000 m. At that point, its engines fail and the rocket goes into free fall, with an acceleration of -9.8 m/s^2
(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 ?
( you will need to consider the motion while the engine is operating and the free-fall motion separatly)

Explanation / Answer

y = v0t +

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