Calculate the energy transferred by rain to each square metre of the surface at a place which receives 100 cm of rain in a year if the average mass of rain drops is $3.0 \times {10}^{-5} \mathrm{kg}$ and their average terminal velocity is 9 m/s.

Average mass of rain drops $\left(\mathrm{m}\right) = 3.0 \times {10}^{-5} \mathrm{kg}$

Average terminal velocity (v) = 9 m/s

Height (h) = 100 cm = 1m

Density of water $\left(\mathrm{\rho }\right)={10}^3\mathrm{kg}/{\mathrm{m}}^3$

Area of the surface (A) = 1 m²

Volume of the water due to rain (v) = Area x height

= A x h

= 1 x 1 = 1 m³

Mass of the water due to rain (M) = Volume x Density

$\begin{array}{l}=\mathrm{V}\times \mathrm{\rho }\\ =1\times {10}^3\\ ={10}^3\mathrm{kg}\end{array}$

$\therefore$ Energy transferred to the surface

$\begin{array}{l}=\frac{1}{2}{\mathrm{mv}}^2\\ =\frac{1}{2}\times {10}^3\times (9{)}^2\\ =40.5\times {10}^3\mathrm{J}\\ =4.05\times {10}^4\mathrm{J}\end{array}$