# Rocket Question - 2 solutions?

• unscientific
In summary, the conversation discusses a rocket leaving a space station in deep space and ejecting fuel at a constant speed. The first part derives an expression for the rocket's position relative to the space station when it has a remaining mass of fuel. The second part discusses the observation of stationary fuel and its implications for the fraction of original mass burnt as fuel. The third part derives an expression for the distance between the space station and the burnt fuel, and calculates a value for this distance given certain parameters. There are two methods presented, with a correction needed for the second method.
unscientific

## Homework Statement

A rocket of initial total mass mi leaves a space station in deep space, far from all sources of gravitation. The rocket ejects burn fuel at a constant speed u << c relative to the rocket.

(a) Derive an expression for the rocket relative to the space station when the total mass of the rocket plus remaining fuel is mf.

(b) Some time after the rocket has left the space station, a small quantity of the ejected fuel remains stationary in the frame of the space station. What limit does this observation place upon the fraction of the original total mass that was burnt as fuel?

(c) The rocket ejects fuel at a rate proportional to its remaining total mass m, so that (dm/dt) = -αm. Derive an expression for the distance x between the space station and the stationary burnt fuel. Obtain a value for x given that u = 1000 ms-1, and that m is reduced to half its starting value after 10 minutes.

## The Attempt at a Solution

Part (a)

Part (b)

Part (c)

Method 1

Method 2

In the second line in method 2, there is "m" missing in the denominator of the right side.
And the units of the result do not match as a consequence.

## What is a "Rocket Question"?

A "Rocket Question" is a hypothetical problem that requires a scientific solution to launch a rocket into space. It is often used as a thought experiment to challenge scientists and engineers to think critically and creatively.

## What are the 2 solutions to the "Rocket Question"?

The 2 solutions to the "Rocket Question" are usually referred to as the "conventional" and "unconventional" solutions. The conventional solution involves using traditional rocket engines and fuel to propel the rocket into space. The unconventional solution involves using alternative methods, such as light or magnetic fields, to launch the rocket.

## Which solution is more feasible?

It is difficult to determine which solution is more feasible without more information about the specific scenario and resources available. However, the conventional solution is currently the most commonly used method for launching rockets into space.

The conventional solution has the advantage of being a well-established and reliable method for launching rockets. However, it also has the disadvantage of being expensive and producing a significant amount of pollution. The unconventional solution has the advantage of potentially being more environmentally friendly and cost-effective, but it may also face technical and practical challenges.

## What potential advancements in technology could impact the "Rocket Question"?

Advancements in technology, such as more efficient rocket engines, alternative fuels, and stronger materials, could impact the "Rocket Question" by making both the conventional and unconventional solutions more feasible and cost-effective. Additionally, advancements in space exploration and colonization could lead to the development of new methods for launching rockets into space.

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