I'm a high school student and I tried to study about terminal velocity and drag force. And I tried to figure out how to increase terminal velocity. An object has terminal velocity when the size of force(which is not the drag force) is same with the size of drag force. But in some cases, we can apply this formula. In these cases, the less dense the object is, the faster terminal velocity is. In other cases, we can apply this formula. In these situations, the denser the object is, the faster terminal velocity is. I would like to ask you What is the difference between these two situations. Or, is there any error in my exploration process or conclusion? (Two formula images are from wikipedia.)
The density in your first equation refers to the density of the fluid your object is moving through. NOT the density of your object. Terminal velocity is when the drag force is just balanced by the gravity force.
