Question

A water fountain on the ground sprinkles water all around it. If the speed of water coming out of the fountain is v, the total area around the fountain that gets wet is:

Answer 1

Step 1: Given parameters

$\text{speed}=\mathrm{v}$

Step 2:To Find:

Area

Step 3: Calculate area:

$$\begin{gathered} \mathrm{A}=\mathrm{\pi }{\left({\text{Range}}_{\max }\right)}^2 \\ =\mathrm{\pi }{\left(\frac{{\mathrm{v}}^2}{\mathrm{g}}\right)}^2 \\ =\frac{{\mathrm{\pi v}}^4}{{\mathrm{g}}^2} \end{gathered}$$

Here, $\mathrm{A}$ is an area, $\mathrm{v}$ its speed and $\mathrm{g}$ is gravitational acceleration.