Question

WHY DOES A RAIN DROP ACHIEVE TERMINAL VELOCITY AFTER FALLING THROUGH A DISTANCE IN AIR

Answer 1

Consider the motion of a rain drop in air.
Understand that the air is a medium that has definite mass distribution, has definite viscosity, behaves like any other fluid offering buoyancy and viscous drag.
During the motion of the rain droplet the forces acting on it would be
(1) Downward force due to its weight.
(2) Upward force due to the buoyancy of air
(3) Upward force due to viscous drag.
Hence, the net force acting on the droplet would be
$mg-Viscousdrag-buoyantforce$
Now understand that the variable force in the above equation is viscous force considering the density of air to be constant.
Viscous force is dependent on instantaneous velocity.
Hence
$m\frac{dv}{dt}=weight-viscousdrag-bouyantforce$

At some instant of time, the net force acting on the droplet becomes zero during its motion so as to attain a constant velocity called terminal velocity.