Solve the problem.
-To approximate the speed of a river, a circular paddle wheel with radius 0.5 feet is lowered into the water. If the current causes the wheel to rotate at a speed of 11 revolutions per minute, what is the speed of the current? If
Necessary, round to two decimal places.
A) 0.06 mph
B) 34.56 mph
C) 0.2 mph
D) 0.39 mph

Question

Quizplus · Accepted Answer

The speed of the current can be found by calculating the circumference of the paddle wheel (which gives the distance traveled in one revolution) and then multiplying by the number of revolutions per minute. The circumference of the wheel is $2\pi r = 2\pi(0.5) = \pi$ feet. At 11 revolutions per minute, the distance traveled per minute is $11\pi$ feet. To convert feet per minute to miles per hour, use the conversion factors $1 \text{ mile} = 5280 \text{ feet}$ and $1 \text{ hour} = 60 \text{ minutes}$. Thus, the speed is $\frac{11\pi \text{ feet/minute} \times 60 \text{ minutes/hour}}{5280 \text{ feet/mile}} \approx 0.39$ mph.

Solve the Problem. -To Approximate the Speed of a River, a Circular Paddle