Begin Usage 3: Physics applications

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Physics Application Ex1

Properties:

* .... remember how to solve separable equations.

* .... have method that we know to solve these equations directly.

The following example is of a Physics differential equation method:

"The operation of a rocket depends upon the law of conservation of momentum as applied to a system of particles, where the system is the rocket plus its ejected fuel." (Serway, 2004)

As can be seen below the momentum before the firing of the rocket depends upon the rocket mass and the mass of the fuel ORIGINALLY. Yet, in order for the rocket to gain speed (or accelerate) it must experience a force from the rocket fuel ignition.

Each particle acts like a tiny bullet from an automatic weapon with each little push. But, the mass of the rocket DECREASES DUE TO THE LOSS IN FUEL PARTICLES. Thus ve is the fuel velocity relative to the rocket. Altogether, the initial momentum is equated to the total final momentum. And, when the equation is simplified, WE USE DIFFERENTIAL EQUATIONS TO SEPARATE THE VARIABLES AND INTEGRATE BOTH SIDES.

And, after the separation of variables we integrate, as stated, below!!

Hopefully you can now see the usefulness of Differential Calculus in real world applications!!!

Use the link below to get back to Differential Equations Part 1 for the next problem on the table.

Back to the start ... D.E. Ex1.