# Modeling rocket displacement

1. Jul 31, 2007

### rwalrus

I'm trying to model (purely for my own edification) the behavior of a rocket (specifically w.r.t. significant mass loss over time). I *think* I have everything correct, but I'm not totally confident with how I'm computing the vertical displacement (assuming no air resistance)

I have the following:
$$m(t) = m_{rocket+fuel} - \dot m t$$
$$v_{rocket}(t) = v_{eject} \cdot ln \left ( m_{rocket+fuel} \over m(t) \right) - g t$$
$${\dot m} = {F_{thrust} \over v_{eject}}$$
$$E_k(t) ={{ m(t) \cdot v(t)^{2} } \over 2}$$

Hopefully so far I'm ok...I'm assuming constant thrust force and eject velocity, which I am given to understand is ok. I'm also neglecting air resistance.

My reasoning is that since I'm starting from 0 velocity, 0 kinetic energy (I know, rotation of the earth, etc. la la la I can't hear you :tongue2:), the total kinetic energy is the work done, so I have distance:
$$d(t) = {E_k(t) \over F_{thrust}}$$

Is there a better way? I'm working (slowly) on integrating v(t), but it's really quite hairy. And my calc (like my physics) is, well, very poor. (i.e. self taught). I have a spreadsheet where I've got some numbers generated by the above, so if it would be helpful to post those, I can do so.