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Rocket Problem

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A test rocket is fired vertically from a well. A catapult boosts it to ground level, where it has a vertical velocity of 60.0 m/s. At ground level, the rocket engine fires, and the rocket accelerate upward with an acceleration of 5.00 m/s2. When the rocket is 800 m above the ground the engine fails, and the rocket goes into free fall, with a downward acceleration of 9.80 m/s2. Eventually, the rocket crashes into the earth's surface. (a) How long is the rocket in motion above the ground? (b) What is the maximum altitude reached by the rocket? (c) What is its velocity when it crashes into the ground?

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At point A, the rocket is moving upward and leave ground level.
At point B, the engine falls and the rocket is still moving upward.
At point C, the rocket reaches its maximum height.
At point D, the rocket falls down to the ground level.

At point A, ...

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