The blades of a windmill sweep out a circle of area
\[
A=2\,\text{m}^2.
\]
The wind is flowing with velocity
\[
V=6\,\text{ms}^{-1}
\]
perpendicular to the circle and the density of air is
\[
\rho=1.2\,\text{kgm}^{-3}.
\]
Then the power of the mill is
Show Hint
For wind energy problems, first find the mass flow rate:
\[
\dot m=\rho AV.
\]
Then use
\[
P=\frac12\dot mV^2
=\frac12\rho AV^3.
\]
This is the kinetic energy carried by air per second.