Question

A rocket, initially at rest, is fired vertically with an upward acceleration of 10m/s². At an altitude of .50km, the engine of the rocket cuts off. What is the maximum altitude it achieves?

Answer 1

Speed at 0.5 km:

$$v=\sqrt{2ah},\\\space\\ H_\text{max}=h+\dfrac {v^2}{2g}=h\bigg(1+\dfrac ag\bigg),\\\space\\ H_\text{max}=500(1+10/9.8)=1010\text{ m}.$$