Final answer:
To estimate the river's current speed, calculate the linear velocity of a paddle wheel's edge, which rotates at a given rate. The result provides the current speed in feet per minute, which can then be converted into meters per second.
Step-by-step explanation:
To approximate the speed of the current of a river using a circular paddle wheel with a radius of 6 ft that rotates at 17 revolutions per minute, we need to calculate the linear velocity at the edge of the paddle wheel. This can be found using the formula for the circumference of a circle (C = 2πr) and by converting the rotational speed to linear speed.
The circumference of the paddle wheel is 2π × 6 ft, which gives us 12π ft per revolution. Multiplying this value by the number of revolutions per minute will give us the distance covered by the paddle wheel in one minute. So, the linear speed of the paddle wheel is 17 revolutions × 12π feet per revolution, which equals 204π feet per minute.
Since the paddle wheel rotates because of the river current, this value also represents the speed of the current in feet per minute. To convert the speed into more common units like feet per second or meters per second, we can use unit conversion factors:
1 foot = 0.3048 meters
The speed of the current is approximately 204π ft/min × (1 min/60 sec) × (0.3048 m/1 ft), which simplifies to a numerical value that gives us the speed of the current in meters per second.