Modelling the motion of a meteor

[PeterH]

Hi!
I am to model the motion of a meteor as it travels through the atmosphere, taking into account the loss of mass, which is 0.025 kg upon impact (height = 0). I also have to take into account the air resistance on the meteor, the fact that the air density is a function of height and that the orthographic projection of the meteor perpendicular the direction of movement (part of the air resistance equation) is a function of the mass of the meteor.
I assume that gravitational field strength is constant.

I have attached a picture of the equations I have been able to derive so far using standard formulas.

I have to solve the differential equations for x(t) and y(t) numerically, however, I fail to see how and therefore seek help.

This is for a very important school project and I'm running out of time, so I really need help. Even the smallest hint would be greatly appreciated!

 

[mfb]

Simply calculate it step by step in small time steps?
You know the initial position and velocity at t=0, you can calculate the acceleration there and use this to estimate the position and velocity at t=0.01s (or whatever). Use the data there to estimate the values for t=0.02s and so on. There are better integration schemes, but start with the easiest one and improve that later if you like.

Your equation for A can be simplified a bit.

The atmospheric density does not follow an exponential law as the temperature depends on height, by the way.

 

[ellipsis]

Newtonian gravity with atmospheric drag is not solvable analytically. Use an ordinary differential equation numerical solver. I prefer MATLAB.

It would help if you tell us what exactly A(m), m(t), etc are. Also, what is that little squiggly variable for? Is it a constant?

 

[PeterH]

This is everything

 

[PeterH]

Mass as a function of time only

 

[mfb]

I don't think that equation for m(t) makes sense, it has m(t) at the right side as well, but multiplied by t and other factors. Looks like a wrong differential equation.