Question

A water wheel has a radius of 9 feet. The wheel is rotating at 5 revolutions per minute. Find the linear​ speed, in feet per​ minute, of the water.

Answer 1

Answer:

$90\pi\text{ ft/s}\approx282.74\text{ ft/s}$

Step-by-step explanation:

Refer to physics equation $v=\omega r$, where $\omega$ is angular velocity.

Angular velocity's SI unit is rad/s. Convert rev/min to rad/s:

$\displaystyle 5\text{ rev/min}=5\cdot \frac{1}{60}\cdot 2\pi\approx 0.524\text{ rad/s}$

Now substitute $\displaystyle\omega=\frac{1\pi}{6}$ and $r=9$ into $v=\omega r$:

$\displaystyle v=\frac{1\pi}{6}\cdot 9=\frac{3}{2}\pi\text{ ft/s}=\boxed{90\pi\text{ ft/s}}$