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How to intergrate a equation for freefall with drag force as kv^2?
I need to work out the displacement of a object in free fall at any point. I know that to do this I need to start from F=ma, and I have F=mg-kv^2 since we have been given that for the most part. I turned the a into a dv/dt, and intergrated everything, but cannot/do not know how to intergrate (ds/dt)^2 which i think is the next step. Any help would be great
2 Answers
- Steve4PhysicsLv 79 years agoFavourite answer
This form of drag is sometimes called 'quadratic drag' because of its dependence on v^2; you can look it up.
As far as I know, this is a bit awkward as integration reqires a hyperbolic function.
There is a powerpoint presentation about this in the 1st link, or if you prefer you can see it via the Google viewer in the 2nd link.
About 1/4 of the way down, you will see section 2.4 is called 'Quadratic Air Resistance'. Look a bit further down and you come to "Vertical Motion with Quadratic Drag" which is what you want. There seems to be a few extra slides inserted for teaching purposes explaining hyperbolic functions.
Hope that helps.
Source(s): http://www.google.co.uk/url?sa=t&rct=j&q=&esrc=s&s... https://docs.google.com/viewer?a=v&q=cache:P28W2Ql...