posted on Sep, 26 2011 @ 07:24 AM
reply to post by kaleshchand
Since you can solve for only one variable at a time, you'd keep your other quantities such as mass of the vessel and it's speed as constants and
solving for the weight of the fuel which is constantly changing at a certain rate as a function of time.
For example at any point in time the mass of your fuel relative to time could be defined as:
Fuel(t) = Total Fuel - Fuel Consumed or
we'd call them ...FT(t) - FC(t)
You'd then Integrate that function ....cant draw integral symbols but you'd have ...
The integral of F(t) dt, or the Integral of FT(t) - FC(t) dt which you would solve by using Integration By Parts* solving each one individually and
then later merging them.
In calculus, and more generally in mathematical analysis, integration by parts is a rule that transforms the integral of products of functions into
other (ideally simpler) integrals. The rule can be derived in one line by simply integrating the product rule of differentiation.
you'd then substitute values of t or conversely you could solve for the time in which all of the fuel was consumed by making Total Fuel = Fuel
Consumed and solving for t (time) at which this occurs.
It would be something along those lines this is just off of the top of my head....
But Check out some Calculus and Physics Texts. You know that Isaac Newton also invented The Calculus in which to solve his Physics problems....but you
need to correlate units which is the essence of solving any math problem.
Integration by parts: