The velocity v(t) of a skydiver falling to the ground is governed by
m dv/dt = mg - kv^2
where m is the skydiver's mass, g is the acceleration due to gravity, k > 0 is the drag
coefficient, and v(t) >= 0.
Solve this equation for v(t) with the initial condition v(0) = 0.
I have been doing other diff equations but when its a word problem it confuses me.. So, i treat m, g and k as constants.
I rearranged equation into this:
dv/dt + (k/m)v^2 = g
so now i can use integrating factor..
mu(x) = e^integ (k/m) ...but im going to stop here already, in case im already on wrong track.. The fact that v is squared changes things, no? (cant use integrating factor?) If this is ok though, i will proceed.. Thanks alot for any help/tips