Solving for c in v(t,g,m,c) given intial v,g,m,t

So I was given the initial equation

m(Dv/dt) = m*g-c*v ; v(0) = 0; [from textbook]

so I solved for v using

v = dsolve('Dv=(m*g-c*v)/m', 'v(0)=0')

and got

v =

(g*m - (g*m)/exp((c*t)/m))/c

now I am given

v = 28, g = 9.81, m =90, t =4

and I am supposed to find c

so I used

   f =subs( v, {g,m,t}, {9.81,90,4)}

then solve(f-28, c)

however, I keep getting a lambertw function in my value for c or some expression including k,pi and i, so I think I must be doing something wrong.

Suggestions?

Answer 1

[Honglei Chen]

Are you looking for a symbolic solution? If you want a numerical one, you can use fzero

v = 28, g = 9.81, m =90, t =4;
fzero(@(c) (g*m - (g*m)/exp((c*t)/m))/c-v, -1)

[Victor]

I am looking for a numerical answer for c.

[Victor]

That worked!

Thank you very much :D