How Fast Will a Rocket Go If It Burns Half Its Mass in Fuel?

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The discussion revolves around calculating the maximum velocity of a 1000kg rocket that burns half its mass in fuel while producing a thrust of 25,000N. The rocket is intended to reach an altitude of 580 km on a planet similar to Earth, without atmospheric resistance. Participants are encouraged to share their calculations and insights on the physics involved, particularly focusing on the rocket's mass loss and the resulting acceleration. The conversation emphasizes the importance of understanding thrust, mass, and gravitational forces in determining the rocket's performance. This analysis ultimately aims to clarify how these factors influence the rocket's maximum velocity.
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**Bonus Question** Gravitation

A 1000kg rocket sits on the surface of a Earth like (same mass and radius - no atmosphere) planet. When fired, the rocket engines produce a force of 25 000N. The rocket is designed to reach an altitude of 580 km before the fuel runs out. If 1/2 of the rockets initial mass is from fuel, then calculate the maximum velocity the rocket achieves.
 
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