ODEs/Physics help

[eestlinc]

well, I never took diff equations so I don't know either way.

[Endless]

Newton's second law:

d(mv)/dt = F
mdv/dt+vdm/dt = F, since m is constant, m*dv/dt = F

m*dv/dt = -m*g - k*v² [k=100, m=100]
100*dv/dt = -100 (g+v&#178
dv/dt = -v²-g
dv/dt = -(dy/dt)²-g

And then, well, we're still stuck. Maybe with G² = g and a = -1
dv/dt = a*(v-Gi)*(v+Gi), with i as in i² = -1
or
dv/dy = -dy/dt - g* dt/dy?

That page (http://www.profjrwhite.com/diff_eqns...es/appls_1.pdf or http://gershwin.ens.fr/vdaniel/Doc-L...w/nwt2law.html) solves it for downward motion.

Edit: forgot to count the 1000000. duh.
So yeah, what kb says below. dv/dt = 10000-v²

[Kirobaito]

I finally figured it out. The net force of 1000000 already includes gravity, so it's just

1000000 - 100v^2 = 100dv/dt

Which becomes

dt = dv/(10000-v^2)

You can separate that into

dv/(100+v)(100-v)

And use partial fractions, where both A and B are equal to 1/200...

dt = dv/200(100+v) + dv/200(100-v)

Take the integral and you get

t = (1/200)(ln|100 + v| - ln|100 - v|)

200t = ln|100+v/100-v|

Put e to both sides:

e^200t = (100+v)/(100-v)

100e^200t - ve^200t = 100+v

100e^200t - 100 = v + ve^200t
100e^200t - 100 = v(1 + e^200t)

v(t) = (100e^200t - 100)/(1+e^200t)

v(t) = 100(e^200t-1)/(1+e^200t)

I'm not sure if you can reduce it more.