Calculate Velocity of Skydiver: Mass M, Air Drag Coefficient D

[Crebble32]

Calculate velocity of the skydiver of mass M= 80kg as a function of time. The air drag coefficient D= 100g/m = 0.1kg/m. Assume that the skydiver has v=o at t=0.


In my book high speed air drag is f=Dv^2.
I found Vt= 88.5 m/s with Sqrt(mg/D). BUT this is not the V they are asking for :(

my book derives the formula for V with the low speed air drag, not the HIGH speed one. I can't follow the steps they did and figure out what exactly the formula actually is! What I started out with is:

m*(dv/dt) = mg- Dv^2

I have no clue where to go from here :( If anyone could help me I appreciate any help I can get!

 

[Stonebridge]

This page goes through the theory for you. It uses drag is proportional to v² and the resulting derivation gives terminal velocity = sq root mg/k [k=drag coefficient]

http://www.intmath.com/Differential-equations/2_Separation-variables.php#skydiving

 

[Crebble32]

Thank you so much!