Advanced Quadratic drag - How to solve?
So I have gotten this far...
#a=((F_a-(c_d*rho_h*A*v^2)/2)-m_t*g_r)#
This is based upon #F_a-(F_d+F_g)/m =a#
But #a# is #(dv)/(dt)#
So this becomes a differential equation because the faster you go the harder it is to go faster.
How can one solve this?
Please note I'm currently a Calc AB student.
So I have gotten this far...
This is based upon
But
So this becomes a differential equation because the faster you go the harder it is to go faster.
How can one solve this?
Please note I'm currently a Calc AB student.
1 Answer
see below
Explanation:
your work looks a little bit messed up. EG It is dimensionally incorrect for starters.
I can see the sense of it, the interaction between Rayleigh drag and gravity. Is there also an additional force that is purporting to act on the mass? i can't figure that out on a quick look.
the DE you get shouldn't be too much trouble, in the sense it should be separable. the problem you will have is the same as with all damping/ friction like effect in that it opposes motion and so you becomes obsessed with the actual sign of v
if you linked the actual prob, that would be helpful
FWIW if you have a situation where a body was free falling in drag, you could say in the vertical x direction, with downward as positive co-ordinate, that
and
that is separable though the solution might not be so sweet
post the question or some more specifics. hope that helps in some way