This is a small part of a problem I'm getting stuck on. I'm going to skip past the beginning steps to a part that I know is correct before I get stuck.
We have a baseball thrown up into the air, with quadratic drag. I'm attempting to solve for an equation of motion y(v).
The Attempt at a Solution
We end up getting an equation
d/dt v = -g[1+(v/v_t)^2]
(I know that this is correct, the book gives it)
where v_t is the terminal velocity. We can then rewrite d/dt v = v dv/dy.
After separating variables, I get
v/[1+(v/v_t)^2] dv = -g dy
I integrate both sides and get
gy = 1/2 v_t^2 ln(v_t^2+v^2)+C
This is really the part where I'm confused. I thought that we can't take the logarithm of a non-unitless number and v_t^2+v^2 is definitely not unitless.