Question

6.1.115 To approximate the speed of the current of a​ river, a circular paddle wheel with radius 4 ft. is lowered into the water. If the current causes the wheel to rotate at a speed of 18 revolutions per​ minute, what is the speed of the​ current?

Answer 1

Answer:

1.2 ft/s or 72 ft/min

Explanation:

To solve this problem, we can use the relationship between the angular and linear speed for this particular movement (rotation). As the speed of the current is tangent to the trajectory of the wheel we can define as follows:

$v= \omega r=18 \frac{rev}{min} \times \frac{1min}{60s}\times 4 ft\\v= 1.2 \frac{ft}{s}= 72 \frac{ft}{min}$

The speed of the current is 72 ft/min