Launched rocket

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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