- #1

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## Homework Statement

I want to try to derive the rocket equation and then add additional effects like gravity, air resistance, etc. Here's the equation that I found online:

## Homework Equations

p (momentum) = mass * velocity

F (force) = Δp / Δt

## The Attempt at a Solution

[/B]

p

_{i}= mv

Here is where the problem is. I do this:

p

_{final}= (m - dm)(v + dv) - dm(v - v

_{e})

But online solutions show that it is either (m + dm) OR + dm(v - v

_{e}), not minus.

Anyways, continuing to solve with my equation gets:

p

_{i}= p

_{final}(conservation of momentum)

mv = (m - dm)(v + dv) - dm(v - v

_{e})

mv = mv + mdv - vdm - dmdv - vdm + v

_{e}dm

Again, here the vdm should cancel, but they dont't.

mdv - dmdv = 2*vdm - v

_{e}dm

Here, I read that dmdv is considered a higher order term so it is negligible.

mdv = dm(2v - v

_{e})

So I got to this point but the equation is wrong. It is obvious that the mass of the rocket time dv (i.e. its change in momentum) doesn't equal the mass of the exhaust times 2v - v

_{e}, it should just be v - v

_{e}. But even that is wrong since it is just dm times v

_{e}. So my question is what am I missing?