- #26

- 33,797

- 5,580

There is no basis for such an equation, and it is certainly wrong.taking $$v=ah+b,$$

An object falling through a dragging medium approaches, but never quite reaches, a "terminal velocity".

The

*exact*relationship to time or distance is not susceptible to algebra - it's very complicated. Typically, drag is roughly a linear function of speed at low speeds, more like a quadratic one at higher speeds.

But we do not need to care about the details here. What matters is that at the start the drag is very small, so v

^{2}is nearly linear with h (the ½v

^{2}line starts tangent to the gh line), but as h increases v

^{2}rises more slowly and approaches a horizontal asymptote.