Question

To approximate the speed of the current of a river, a circular paddle wheel with radius 4 feet is lowered into the water. If the current causes the wheel to rotate at a speed of 10 revolutions per minute, what is the speed of the current? Express your answer in miles per hour.

Name: Problem 115, Chapter 7: Algebra and Trigonometry
Uploaded: 2020-06-15T16:55:41-08:00
Duration: 1 min 25 s
Channel: Katelyn Chen
Description: To approximate the speed of the current of a river, a circular paddle wheel with radius 4 feet is lowered into the water. If the current causes the wheel to rotate at a speed of 10 revolutions per minute, what is the speed of the current? Express your answer in miles per hour.

   To approximate the speed of the current of a river, a circular paddle wheel with radius 4 feet is lowered into the water. If the current causes the wheel to rotate at a speed of 10 revolutions per minute, what is the speed of the current? Express your answer in miles per hour.

Algebra and Trigonometry

Michael Sullivan 10th Edition

Chapter 7, Problem 115

Instant Answer

Solved by Expert Katelyn Chen

06/15/2020

Step 1

This is the circumference of the circle, which is given by the formula $2\pi r$, where $r$ is the radius of the circle. In this case, the radius is 4 feet, so the circumference is $2\pi(4) = 8\pi$ feet. Show more…

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To approximate the speed of the current of a river, a circular paddle wheel with radius 4 feet is lowered into the water. If the current causes the wheel to rotate at a speed of 10 revolutions per minute, what is the speed of the current? Express your answer in miles per hour.

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Key Concepts

Angular and Linear Motion Relationship

This concept involves understanding how an object's linear velocity along a circular path is related to its angular speed. Specifically, linear speed can be found by multiplying the angular speed (in revolutions per unit time) by the circumference of the circle, which represents the distance traveled per revolution.

Circle Geometry and Circumference

The circumference of a circle is the linear distance around the circle and can be calculated using the formula C = 2?r, where r is the radius. This key geometric property is essential when calculating distances traveled in one full rotation of a circular object.

Unit Conversions

Unit conversion is the process of converting a measured value from one unit to another. In many physics and engineering problems, such as converting feet per minute to miles per hour, it is crucial to apply the correct conversion factors to ensure that the final answer is expressed in the desired units.

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