I have an assignment, where I’m required to derive the formula for air resistance for a falling object.
$$ F = \frac{1}{2}CAdv^2 $$
where $C$ is drag coefficient, $A$ is the cross-sectional area, $d$ is the density of the air and $v$ is the speed, through dimensional analysis.
In the process, I’m required to explain why the air resistance on the object is independent of the mass, $m$, and the position, $x$, of the object. However, I can’t really explain why that is? How do I clearly explain and prove, that those things do not have an effect on the air resistance?
Edit
Now I have a pretty good understanding of why air resistance is independent of mass, since it's actually quite straight forward. However, something that is not so straight forward, is explaining why air resistance is also independent of acceleration, $a$. How would you convince someone, that this is the case, because I don't see a clear way of doing that?