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Chapter 52: Chapter 52

Problem 909

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If an observer could be suspended in the same spot in space over the equator and watch the world turn, how many miles of the equator would he observe to pass by in 1 hour?

Short Answer

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The observer would witness approximately 1037.54 miles of the equator pass by in 1 hour.
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TABLE OF CONTENTS :
TABLE OF CONTENTS

Step 1: Understand the problem

This problem can be solved by understanding that the observer standing over the equator will be witnessing the rotation of the earth underneath them. Considering that the earth completes one full rotation (360 degrees) in a day (24 hours), we need to find out how far the earth rotates per hour.

Step 2: Find the Earth's Circumference

Earth’s Equator is almost a perfect circle. Therefore, the best way to calculate the distance around the earth (its circumference) is by using the formula \(C = 2 \pi r\), where \(r\) is the radius of earth. According to NASA, Earth's equator radius is about 3965 miles. So, the earth's circumference is \(C = 2 \pi \times 3965 = 24901\) miles.

Step 3: Find the Distance Travelled in 1 Hour

We know that the earth completes one full rotation (360 degrees) in 24 hours. Therefore, in 1 hour, the earth will cover \(\frac{1}{24}^{th}\) of its circumference. Let's call the distance covered in an hour as \(d\). Therefore, \(d = \frac{C}{24} = \frac{24901}{24} = 1037.54\) miles. So the observer would witness approximately 1037.54 miles of the equator pass by in 1 hour.

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Most popular questions from this chapter

Chapter 52

The surface area of a sphere is \(4 \pi \mathrm{r} 2\), where \(\mathrm{r}\) is the radius of the sphere. Assuming that the diameter of the earth is 800 miles and \(\pi=22 / 7\), what is the surface area of the earth?
Chapter 52

Bellingham, Washington, is at \(49^{\circ} \mathrm{N}\) latitude and \(122^{\circ} \mathrm{W}\) longitude. San Francisco, California is at \(38^{\circ} \mathrm{N}\) latitude and \(122^{\circ} \mathrm{W}\) longitude. What is the direct air distance from Bellingham to San Francisco?
Chapter 52

New York City has longitude \(74^{\circ} \mathrm{W}\) and Portland, Oregon has longitude \(122^{\circ} \mathrm{W}\). (a) What is the difference in longitude between these 2 cities? (b) What fraction of \(360^{\circ}\) is this? (c) What is the actual time difference between New York City and Portland?
Chapter 52

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Chapter 52

How far apart are 2 points on the equator if their longitudes differ by \(1^{\circ} ?\)
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