Consider a particle in a gravitational field that is also subject to a resisting force proportional to the velocity squared ( Fdrag = + or - cv2).
a) Find the terminal velocity, vT, for the object as it falls.
b) Show that for an object dropped from rest that the velocity is given by v = vTtanh-1(-t/β)
where β = sqrt( m/gc )
The Attempt at a Solution
I did part a and got vT = sqrt( mg/c )
but for part b I am not getting the same result that is shown.
My work is shown in the attachment (the tau in the attachment is the β. I wrote it as β here because its hard to distinguish the t, T, and the tau on here)