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Chapter 1: Problem 64

The distance from Earth to the Moon is approximately \(240,000 \mathrm{mi}\). (a) What is this distance in meters? (b) The peregrine falcon has been measured as traveling up to \(350 \mathrm{~km} / \mathrm{hr}\) in a dive. If this falcon could fly to the Moon at this speed, how many seconds would it take? (c) The speed of light is \(3.00 \times 10^{8} \mathrm{~m} / \mathrm{s}\). How long does it take for light to travel from Earth to the Moon and back again? (d) Earth travels around the Sun at an average speed of \(29.783 \mathrm{~km} / \mathrm{s}\). Convert this speed to miles per hour.

Short Answer

Expert verified
(a) The distance from Earth to the Moon in meters is approximately 386,160,000 meters. (b) It would take the falcon about 3,970,000 seconds to fly to the Moon at its maximum speed. (c) It takes light about 2.5744 seconds to travel from Earth to the Moon and back. (d) Earth travels around the Sun at an average speed of about 66,614 miles per hour.

Step by step solution

01

(a) Convert distance to meters

To convert miles to meters, use the conversion factor: 1 mile ≈ 1,609 meters. Therefore, the distance from Earth to the Moon in meters can be calculated as follows: \(240,000~\text{miles} \times 1,609~\frac{\text{m}}{\text{mile}} = 386,160,000~\text{m}\). So, the distance from Earth to the Moon is approximately 386,160,000 meters.
02

(b) Time taken by the falcon to reach the Moon

First, we need to convert the falcon's speed to meters per second: \(350~\frac{\mathrm{km}}{\mathrm{hr}} \times \frac{1,000~\mathrm{m}}{1~\mathrm{km}} \times \frac{1~\mathrm{hr}}{3,600~\mathrm{s}} = 97.222~\frac{\mathrm{m}}{\mathrm{s}}\). Now, we can calculate the time it takes for the falcon to fly to the Moon: \(\text{Time} = \frac{\text{Distance}}{\text{Speed}} = \frac{386,160,000~\mathrm{m}}{97.222~\frac{\mathrm{m}}{\mathrm{s}}} = 3,970,000~\text{s}\). So, it would take the falcon about 3,970,000 seconds to fly to the Moon at its maximum speed.
03

(c) Time taken for light to travel to the Moon and back

To find the time taken for light to travel to the Moon and back, we can use the formula: \(\text{Time} = \frac{\text{Distance}}{\text{Speed}}\). The speed of light is given as 3.00 × 10^8 m/s, and the distance is doubled since light needs to travel to the Moon and back: \(\text{Time} = \frac{2 \times 386,160,000~\mathrm{m}}{3.00 \times 10^8~\frac{\mathrm{m}}{\mathrm{s}}} = 2.5744~\text{s}\). So, it takes light about 2.5744 seconds to travel from Earth to the Moon and back.
04

(d) Convert Earth's speed to miles per hour

To convert the Earth's speed from kilometers per second to miles per hour, we can use the following conversion factors: 1 mile ≈ 1.609 kilometers, and 1 hour ≈ 3,600 seconds: \(29.783~\frac{\mathrm{km}}{\mathrm{s}} \times \frac{1~\mathrm{mile}}{1.609~\mathrm{km}} \times \frac{3,600~\mathrm{s}}{1~\mathrm{hr}} = 66,614~\frac{\mathrm{mi}}{\mathrm{hr}}\). So, Earth travels around the Sun at an average speed of about 66,614 miles per hour.

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Most popular questions from this chapter

(a) The diameter of Earth at the equator is \(7926.381 \mathrm{mi}\). Round this number to three significant figures, and express it in standard exponential notation. (b) The circumference of Earth through the poles is \(40,008 \mathrm{~km}\). Round this number to four significant figures, and express it in standard exponential notation.

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