Originally posted by JirakonHad to look at this one for a while, but I finally got something simple:
It's been a while since I've done differential equations...
v'(t) - k [v(t)]^2 = g
Solve for v(t).
I'd know what to do if the v weren't squared, but I have no idea what to do here.
v'(t) = k[v(t)]^2 + g = (SQRT(k)*v + i*SQRT(g)) * (SQRT(k)*v - i*SQRT(g))
Putting this into a more useable form, we have:
dv / ((SQRT(k)*v + i*SQRT(g)) * (SQRT(k)*v - i*SQRT(g))) = dt
Now just separate the fractions and integrate each one. I have to split, but the answer should follow simply from here. (If no one finishes it, I'll do it when I get home.)
Originally posted by JirakonI dropped the v dependence in t in intermediary calculations for the sake of a lighter notation.
It's been a while since I've done differential equations...
v'(t) - k [v(t)]^2 = g
Solve for v(t).
I'd know what to do if the v weren't squared, but I have no idea what to do here.
http://i35.tinypic.com/5bv0h5.gif
Originally posted by adam warlockI forgot to add the constant of integration so the last two steps should be -1/v=kt+C which implies v(t)=-1/(kt+C) where C depends on the initial conditions
I dropped the v dependence in t in intermediary calculations for the sake of a lighter notation.
http://i35.tinypic.com/5bv0h5.gif
Originally posted by adam warlockEnjoy!
Shamed as I am of admitting it, but it isn't LateX. It was done using MathType and then I exported the solution into a .gif image.
I wasn't at my machine and so couldn't use LateX.
😳 😳 😳
http://thornahawk.unitedti.org/equationeditor/equationeditor.php