Launched rocket

Classical Mechanics Level 2

A rocket, initially at rest on the ground, accelerates straight upward at a constant acceleration of $$a$$ for a time period of $$t_{1}$$ until the fuel is exhausted. Then, after reaching the highest point, the rocket falls freely. What is the maximum height reached by the rocket?

Ignore the air resistance.
Assume a constant acceleration of $$-g$$ due to gravity during the freefall.

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