Tuesday
September 30, 2014

Homework Help: Differential Equations

Posted by Erica on Thursday, January 24, 2013 at 12:58am.

The velocity v of a freefalling skydiver is well modeled by the differential equation
m*dv/dt=mg-kv^2
where m is the mass of the skydiver, g is the gravitational constant, and k is the drag coefficient determined by the position of the driver during the dive.

(a)Find the general solution of the differential equation.

(b) Calculate the limit of v(t) as t -> INF.

I just started with dv/dt=g-(k/m)v^2 I dont really know where to go from there. Tried integrating dv/(g-(k/m)v^2) but I get stucked.

The answer for (a) is supposed to be v(t) = sqrt(m/(kv)*(Ce^(2*sqrt(kg/m)*t)-1)/(Ce^(2*sqrt(kg/m)*t)+1)

and for (b)sqrt (mg/k)

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