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Chapter 1: Problem 10

Until 1883 , every city and town in the United States kept its own local time. Today, travelers reset their watches only when the time change equals \(1.0 \mathrm{~h}\). How far, on the average, must you travel in degrees of longitude between the time-zone boundaries at which your watch must be reset by \(1.0 \mathrm{~h} ?\) (Hint: Earth rotates \(360^{\circ}\) in about \(24 \mathrm{~h}\).)

Short Answer

Expert verified
You must travel 15 degrees of longitude for a 1-hour change in time.

Step by step solution

01

Understanding Earth's Rotation

The Earth completes one full rotation of 360 degrees in approximately 24 hours. This means the entire globe experiences a full cycle of day and night over this period.
02

Calculating Degrees per Hour

Since the Earth rotates 360 degrees in 24 hours, we calculate how many degrees it rotates in one hour by dividing these two numbers:\[ \frac{360^\circ}{24 \text{ hours}} = 15^\circ \text{ per hour}. \]
03

Time Zone Adjustment

Travelers change their watch by 1 hour every time they cross a zone with a time difference. Given that each hour corresponds to a 15-degree change in longitude, you must travel 15 degrees of longitude to see a 1-hour change in time.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Earth's Rotation
Earth鈥檚 rotation is a natural phenomenon that affects time and day-night cycles. The planet spins around its axis, completing one full spin approximately every 24 hours.
This rotation is responsible for the succession of daylight and darkness. As different parts of the Earth's surface move in and out of sunlight, we experience day and night.
This continuous movement is why different parts of the world experience sunrises and sunsets at varying times.
The rotational speed has remained relatively constant over millions of years, making it a reliable measure for dividing our hours and ultimately for creating time zones.
Longitude
Longitude is a geographic coordinate that specifies the east-west position of a point on the Earth's surface.
It is measured in degrees, with the Prime Meridian in Greenwich, England being at 0掳 longitude. Longitude lines run from the North Pole to the South Pole.
  • They are circular, meaning they meet again at both poles, unlike latitude lines that run parallel to each other.
  • Longitude helps in determining time differences because the Earth rotates 360掳 in approximately 24 hours.
  • This means every degree of longitude represents a time change of four minutes (since 360 degrees divided by 24 hours results in 15 degrees per hour).
The concept of longitude is crucial for navigation and for setting time zones across the globe.
Time Difference
The time difference is the deviation in hours or minutes from a reference point, often linked to longitude.
Due to Earth's rotation, different longitudes experience solar noon (the point when the sun is highest in the sky) at different times.
This variation leads to the concept of time differences across various geographic locations.
If you move eastward or westward, you experience a change in local time because the Earth rotates at 15掳 per hour.
  • This results in a one-hour time change for each 15掳 of longitude you travel.
  • Countries use these differences to organize time zones, keeping days aligned with sunlight hours.
Understanding these differences is key for international travel and coordinating across time zones.
Time Calculation
Time calculation based on longitude involves determining how much one's local time differs from another's by evaluating their positions on the Earth鈥檚 surface.
If you know the rotation speed of the Earth and the distance in longitude between locations, you can easily compute time differences.
The Earth rotates 360掳 in 24 hours, which means it rotates 15掳 every hour.
To calculate the time change, simply multiply the number of longitude degrees by 4 (as every degree accounts for four minutes).
  • For example, if traveling across 45掳 of longitude, the time difference would be 3 hours (because 45掳 / 15掳 per hour = 3 hours).
  • This method is an efficient way to understand how time zones operate globally, ensuring you can adjust your timekeeping devices accurately.
This simple mathematical approach makes global communication and travel much more manageable.

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Most popular questions from this chapter

The cubit is an ancient unit of length based on the distance between the elbow and the tip of the middle finger of the measurer. Assume that the distance ranged from 43 to \(53 \mathrm{~cm}\), and suppose that ancient drawings indicate that a cylindrical pillar was to have a length of 9 cubits and a diameter of 2 cubits. For the stated range, what are the lower value and the upper value, respectively, for (a) the cylinder's length in meters, (b) the cylinder's length in millimeters, and (c) the cylinder's volume in cubic meters?

The description for a certain brand of house paint claims a coverage of \(460 \mathrm{ft}^{2}\) /gal. (a) Express this quantity in square meters per liter. (b) Express this quantity in an SI unit (see Appendices \(A\) and \(\mathrm{D}\) ). (c) What is the inverse of the original quantity, and (d) what is its physical significance?

\(5 \mathrm{SM}\) Earth is approximately a sphere of radius \(6.37 \times 10^{6} \mathrm{~m}\). What are (a) its circumference in kilometers, (b) its surface area in square kilometers, and (c) its volume in cubic kilometers?

Earth has a mass of \(5.98 \times 10^{24} \mathrm{~kg}\). The average mass of the atoms that make up Earth is \(40 \mathrm{u}\). How many atoms are there in Earth?

Antarctica is roughly semicircular, with a radius of \(2000 \mathrm{~km}\) (Fig. \(1-5\) ). The average thickness of its ice cover is \(3000 \mathrm{~m}\). How many cubic centimeters of ice does Antarctica contain? (Ignore the curvature of Earth.)
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