# Rocket Burning fuel causing change in mass

1. ### kaikalii

17
I made up a scenario: Let's say I have a rocket at rest in space. The rocket initially weighs 100 kg, 50 kg of which is fuel. If the fuel burns at a constant rate of 1 kg/s and produces a thrust of 100 N out the back of the rocket, what will the rocket's velocity be after it runs out of fuel?

From F=ma and V=v0+at, I derived V=Ft/m. The force is 100 N, and it would take 50 s to burn 50 kg of fuel at 1 kg/s, so it would be V=100*50/m.

My question is: What would I use for the mass, since it is changing at the fuel burns? When I assumed that it was just the average mass, 75 kg, I got the final velocity ≈ 66.7 m/s. Am I supposed to just use the average mass since the fuel is burned at a constant rate? Does rocket fuel in the real world burn at a constant rate, or exponentially? If it was exponential, could I just use calculus to find the average mass and then plug it in?

### Staff: Mentor

What you are asking about is known as the "Rocket Equation". Here is a tutorial from NASA:

http://exploration.grc.nasa.gov/education/rocket/rktpow.html

3. ### MrAnchovy

665
You need to use ## 50 + 50 ( 1 - \frac{t}{50} ) ##. Because the acceleration is not constant, you cannot use V=v0+at or work with an average mass though: you need to integrate a differential equation.
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