Launched rocket

Classical Mechanics Level 2

A rocket, initially at rest on the ground, accelerates straight upward at a constant acceleration of a a for a time period of t 1 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 -g due to gravity during the freefall.

1 2 a t 1 2 ( 1 + a 2 g ) \frac{1}{2}at_{1}^{2} \left( 1+ \frac{a}{2g} \right) 1 2 a t 1 2 ( 1 + a g ) \frac{1}{2}at_{1}^{2} \left( 1+ \frac{a}{g} \right) 1 4 a t 1 2 ( 1 + g a ) \frac{1}{4}at_{1}^{2} \left( 1+ \frac{g}{a} \right) 1 2 a t 1 2 ( 1 + g a ) \frac{1}{2}at_{1}^{2} \left( 1+ \frac{g}{a} \right)

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Srinivasa Satti by Srinivasa Satti

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