Air Drag and the Time to Fall
Falling Under Air Drag A classic physics problem is to compute the time $t$ it takes for a particle to fall from a height $h$, under the influence of gravity and air resistance. This problem can, perhaps surprisingly, be solved analytically with only a handful of steps. Let’s assume a particle dropped from rest (initial velocity zero), subject to gravity $g$ and a drag force proportional to $v |v|$. That is, the force can be written as...