## Rocket problem

One of my weaknesses has been interpreting a physics word problem into math. Wanting to practice this, I thought I’d tackle a problem I’d seen before, the rocket problem, from scratch, knowing I could always look up a version of it in Halliday and Resnik.

Assuming a rocket with no exterior forces acting on it, propelling itself by chemical combustion with a constant force . Fully fueled, the rocket weighs , and it is burning fuel at a constant rate of . This gives us an equation for the mass as a function of time, and the acceleration

Integrating both sides by once yields

Integrating a second time yields

I learned several things from working on this.

1) that I understood that I could set up a system of first-order ODEs

2) I was surprised that the velocity was not proportional to t

I think it will be useful to watch some of the MIT open course math lectures, especially this one on solving first order linear ODEs.

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**Tags:** Physics

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