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## Main Question or Discussion Point

Hi I'm Matt,

I'm new to the Physics Forum and this is my first Post so i'm sorry I don't know how to write out maths on here. I'm doing an A-level differential equations project and I decided to make it a bit more real worldy... maybe a mistake. I am modelling a skydiver in freefall (for the skydivers' velocities) and have got some real GPS data of velocities of the freefall. My project has an initial model and an updated model.

My initial model was using the drag force as 1/2(C)(A)(Rho)v

I decided to make the air density a variable for my updated model. I have modelled this as

Rho = P/(RT) where P is the pressure

T is the temperature

R is the gas constant

The plan originally was to solve the final equation using the finite element method for solving second order differentials and then use the central difference method for finding the velocities. Unfortunately I have found that very hard as my text book has no notes on dealing with equations with (ds/dt)

Any help solving this would be greatly greatly appreciated (and sorry for the huge amount of text)

The Equation I am working with: (any thing dashed e.g. v' is differentiated with respect to t)(b is a constant, as is D)

mv' = mg - (1/2)(C)(A)(P

mv' = mg - De

where D = (1/2)(C)(A)(P

Thanks,

Matt

I'm new to the Physics Forum and this is my first Post so i'm sorry I don't know how to write out maths on here. I'm doing an A-level differential equations project and I decided to make it a bit more real worldy... maybe a mistake. I am modelling a skydiver in freefall (for the skydivers' velocities) and have got some real GPS data of velocities of the freefall. My project has an initial model and an updated model.

My initial model was using the drag force as 1/2(C)(A)(Rho)v

^{2}(keeping the shape factor, the area and the density constant) and it wasn't too difficult really, just rearranging and some integration. The model was clearly wrong though since that model has a terminal velocity but the skydivers' velocities had a slow decrease towards the end and the initial accelaration of my skydivers in the model was not enough.I decided to make the air density a variable for my updated model. I have modelled this as

Rho = P/(RT) where P is the pressure

T is the temperature

R is the gas constant

The plan originally was to solve the final equation using the finite element method for solving second order differentials and then use the central difference method for finding the velocities. Unfortunately I have found that very hard as my text book has no notes on dealing with equations with (ds/dt)

^{n}. It also only shows examples when s, s' and s'' are in seperate terms rather than multiplied together.Any help solving this would be greatly greatly appreciated (and sorry for the huge amount of text)

The Equation I am working with: (any thing dashed e.g. v' is differentiated with respect to t)(b is a constant, as is D)

mv' = mg - (1/2)(C)(A)(P

_{0}/(RT_{0}))e^{bs}v^{2}mv' = mg - De

^{bs}vwhere D = (1/2)(C)(A)(P

_{0}/(RT_{0}))Thanks,

Matt