I'm the only person in my ODEs class to have not taken a physics class, and my teacher always forgets that. Trying to do it myself, I can't separate this equation and my head isn't in a variable-separating mode. Help plz.
A rocket of mass 100 kg is fired straight up with a net force of 1,000,000 newtons. It experiences air friction f = -100(ns^2/m^2)v^2. At t=0, v=0, y=0. Assume the mass of the rocket does not change.
a) Write Newton's second law for the rocket.
b) Solve analytically for V(t).
c) Use the answer in part b) and let v = dy/dt. Solve for y(t) using the ODE mode on the calculator. Neatly sketch y(t) for [0,20].
I can do C, except I'm not sure if I'm doing a) right and I can't seem to do b).
a) f = ma
Would you just subtract the air friction from the net force, so it's 1000000 - 100v^2 = 100dv/dt? That's what I did.
b) 1000000 = 100(dv/dt + v^2)
10000=dv/dt + v^2
I can't seem to separate it from here. I'm probably just MISSING something completely obvious, but I can't seem to think straight.
Any help, from those who have taken advanced Calc?