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 v2 is nearly linear with h (the ½v2 line starts tangent to the gh line), but as h increases v2 rises more slowly and approaches a horizontal asymptote.