A catapult launches a test rocket vertically upward from a

Question

Solve the all parts of given question:

Question: A catapult launches a test rocket vertically upward from a well, giving the rocket an initial speed of 79.2 m/s at ground level. The engines then fire, and the rocket accelerate upward at 3.90 m/s2 until it reaches an altitude of 1100 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.)

Part A: For what time interval is the rocket in motion above the ground?

s

Part B: What is its maximum altitude?

km

Part C: What is its velocity just before it hits the ground?

m/s

I know the correct answer for above problem but explain how to get this answer! Thanks.