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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 to reset your watch by 1 hour.

Step by step solution

01

Understanding the Earth's Rotation

The Earth rotates through 360 degrees in 24 hours. This means that each degree corresponds to a certain amount of time.
02

Calculating Degrees per Hour

To find out how many degrees correspond to a 1-hour change, divide the total degrees of Earth's rotation by the total hours in a day. This gives us:\[\frac{360^\circ}{24\, \text{hours}} = 15^\circ/\text{hour}\]
03

Conclusion

On average, you must travel 15 degrees of longitude to reset your watch by 1 hour. This is because the Earth rotates 15 degrees each hour.

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Key Concepts

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

Earth's Rotation
To understand why we need to adjust our watches while traveling across time zones, let's explore the concept of the Earth's rotation. Our planet rotates continuously, completing one full spin, which is 360 degrees, in about 24 hours. This rotation is the reason we experience day and night. As the Earth spins, different parts are exposed to sunlight, creating the cycle of day turning into night.

Think of the Earth as a huge sphere spinning in space. This sphere completes a full rotation around its axis every day. This is why we see the sun rise in the east and set in the west, as the rotation causes the sun to appear to move across the sky. The concept of Earth's rotation is fundamental to timekeeping and helps us synchronize our daily activities with the cycle of daylight and darkness.

Because our clocks are set to this rotation, understanding Earth's movement becomes essential when discussing time zones and longitude.
Degrees of Longitude
Longitude lines are imaginary vertical lines that run from the North Pole to the South Pole. These lines help us determine our position east or west across the globe. There are 360 degrees of longitude, marked from the Prime Meridian (0° longitude) in Greenwich, England.

Each line of longitude represents a specific angle from the Prime Meridian. Think of them as slices of an orange; each slice widens as it goes from the core to the outer edge. These degrees are crucial for navigation and timekeeping. Time zones are based on these lines, dividing the Earth into sections where the local time is the same.

Understanding how degrees of longitude relate to time is essential for calculating time differences as you move east or west. This direct link between location and time stems from the Earth's rotation, dividing the planet into specific time zones.
Time Calculations
Time calculations across different longitude degrees are based on the Earth's rotation. As the Earth rotates 360 degrees in 24 hours, each hour corresponds to a rotation of 15 degrees. This is calculated by dividing the total degrees by the total hours: \[\frac{360^{\circ}}{24 \, \text{hours}} = 15^{\circ}/\text{hour}\]As your location moves east or west by 15 degrees, it effectively changes by one hour in time. So, resetting your watch typically means you've traveled across a boundary separating one time zone from the next. This travel usually spans 15 degrees of longitude.

This concept is handy for travelers who must adjust their clocks as they cross different regions worldwide. Knowing how to calculate these differences enhances not just travel convenience but also our understanding of global time coordination, which relies on converting longitude differences into time differences efficiently.

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Most popular questions from this chapter

The common Eastern mole, a mammal, typically has a mass of \(75 \mathrm{~g}\), which corresponds to about \(7.5\) moles of atoms. (A mole of atoms is \(6.02 \times 10^{23}\) atoms.) In atomic mass units (u), what is the average mass of the atoms in the common Eastern mole?

An old manuscript reveals that a landowner in the time of King Arthur held \(3.00\) acres of plowed land plus a livestock area of \(25.0\) perches by \(4.00\) perches. What was the total area in (a) the old unit of roods and (b) the more modern unit of square meters? Here, 1 acre is an area of 40 perches by 4 perches, 1 rood is an area of 40 perches by 1 perch, and 1 perch is the length \(16.5 \mathrm{ft}\).

Suppose that, while lying on a beach near the equator watching the Sun set over a calm ocean, you start a stopwatch just as the top of the Sun disappears. You then stand, elevating your eyes by a height \(H=1.70 \mathrm{~m}\), and stop the watch when the top of the Sun again disappears. If the elapsed time is \(t=11.1 \mathrm{~s}\), what is the radius \(r\) of Earth?

Iron has a density of \(7.87 \mathrm{~g} / \mathrm{cm}^{3}\), and the mass of an iron atom is \(9.27 \times 10^{-26} \mathrm{~kg}\). If the atoms are spherical and tightly packed, (a) what is the volume of an iron atom and (b) what is the distance between the centers of adjacent atoms?

A ton is a measure of volume frequently used in shipping, but that use requires some care because there are at least three types of tons: A displacement ton is equal to 7 barrels bulk, a freight ton is equal to 8 barrels bulk, and a register ton is equal to 20 barrels bulk. A barrel bulk is another measure of volume: 1 barrel bulk \(=0.1415 \mathrm{~m}^{3}\). Suppose you spot a shipping order for "73 tons" of M\&M candies, and you are certain that the client who sent the order intended "ton" to refer to volume (instead of weight or mass, as discussed in Chapter 5 ). If the client actually meant displacement tons, how many extra U.S. bushels of the candies will you erroneously ship if you interpret the order as (a) 73 freight tons and (b) 73 register tons? \(\left(1 \mathrm{~m}^{3}=28.378 \quad\right.\) U.S. bushels.)

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