Clouds

Clouds can hold an enormous amount of water. When this water falls as rain it clearly has a significant mass so why don't clouds fall? In fact, the small water droplets that make up clouds do fall slowly. However, the drag force of the air dominates over the gravitational force for small particles. The drag force increases as the size of an object decreases. The force needed to move a small sphere through a viscous medium is given by Stokes's law, $\vec{F} = -6\pi \eta R\vec{v}$.

Here, $R$ is the radius of the sphere, $\vec{v}$ is the velocity, and $\eta$ is the viscosity. The viscosity of air is 0.018×10^-3 Pa s.

A water droplet with a radius of $R =$  nm starts to fall from rest at $t=0$. What is the maximum velocity of this droplet?

The density of water is 1 g/cm³. The acceleration of gravity is $g=9.81$ m/s².

Second order linear differential equation solver.