For an object with cross-sectional area $A$ moving at speed $v$ through a fluid of density $\rho$, the drag force $D$ is given by $D = \frac{1}{2} C \rho A v^2$, where $C$ is a constant. Show that $C$ has no unit.
A raindrop drops vertically from rest. Assume that air resistance is negligible. On Fig. 1.1, sketch a graph to show how the velocity $v$ of the raindrop varies with time $t$ during the first $1.0\,\text{s}$ of motion.
Calculate the velocity of the raindrop after it has fallen $1000\,\text{m}$.
State an equation that connects the forces acting on the raindrop when it is falling at terminal velocity.
The raindrop has mass $1.4 \times 10^{-5}\,\text{kg}$ and cross-sectional area $7.1 \times 10^{-6}\,\text{m}^2$. The density of the air is $1.2\,\text{kg m}^{-3}$ and the initial velocity of the raindrop is zero. The value of $C$ is $0.60$. Show that the terminal velocity of the raindrop is about $7\,\text{m s}^{-1}$.
The raindrop attains terminal velocity after falling about $10\,\text{m}$. On Fig. 1.1, sketch the way velocity $v$ changes with time for the raindrop. The sketch should show the first $5\,\text{s}$ of the motion.