Intro to Differential Equations question.
I've tried this problem a few times and am not sure if I actually got what they are asking for. I am in the process of latex-ing this out so I can put my work down here so you can see it. For now, here's the problem and of course any help is much much appreciated.
A skydiver with mass "m" jumps from a very large height. The only forces acting on him are the earth's gravitational pull (mg, where g=9.8m/s^2) and a retarding force due to air resistance, which is proportional to the velocity "v". Since F=ma and a=dv/dt, we then have the differential equation m(dv/dt)=mg-kv (k is constant)
I) Solve the differential equation for v.
II) Find the limit of v(t) as t approaches infinity, the skydivers terminal velocity.