Question

To approximate the speed of a river, a circular paddle wheel with radius 0.68 feet is lowered into the water. If the current causes the wheel to rotate at a speed of 14 revolutions per minute, what is the speed of the current? Express the answer in miles per hour rounded to two decimal places, if necessary.
A)0.68 miles per hour

B)59.82 miles per hour

C)0.11 miles per hour

D)0.34 miles per hour

Answer 1

This is a complicated question because part of the paddle is submerged, so the effective radius is somewhat less than r=0.68 feet.  We'll ignore that.

We have f=14 revolutions per minute so the tip of our paddles moves at

$v = 2\pi r f$

That's it except we'll get the result in feet per minute which we have to convert to mph.

$v= 2\pi(0.68\textrm{ feet} )(14 \textrm{ per minute}) \times \dfrac{1 \textrm{ mile}}{5280 \textrm{ feet}} \times \dfrac{60 \textrm{ minutes}}{\textrm{hour}}$

$v = 0.679726 \textrm{ miles per hour}$

Answer: A

That's oddly close to the radius in feet because $2\pi(14)(60)\approx 5278$.