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Chapter 1: Problem 73

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 \(350 \mathrm{~km} /\) 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 386,241,600 m. (b) It would take the peregrine falcon approximately 3,972,299.27 seconds to fly to the Moon. (c) It takes light approximately 2.57 seconds to travel from Earth to the Moon and back again. (d) Earth travels around the Sun at an average speed of approximately 66,616.26 miles per hour.

Step by step solution

01

Part (a): Convert distance from miles to meters

To convert the distance from miles to meters, we can use the conversion factor: 1 mile = 1609.34 meters. \(240,000 \ \mathrm{mi} \times \frac{1609.34 \ \mathrm{m}}{1 \ \mathrm{mi}} = 386,241,600 \ \mathrm{m} \) The distance from Earth to the Moon is approximately 386,241,600 meters.
02

Part (b): Calculate the time it takes for the peregrine falcon to travel to the Moon

To find the time it takes for the falcon to travel to the Moon at a speed of 350 km/hr, we can use the formula: time = distance / speed. First, we need to convert the falcon's speed to meters per second. \(350 \ \frac{\mathrm{km}}{\mathrm{hr}} \times \frac{1000 \ \mathrm{m}}{1 \ \mathrm{km}} \times \frac{1 \ \mathrm{hr}}{3600 \ \mathrm{s}} = 97.22 \ \frac{\mathrm{m}}{\mathrm{s}} \) Now we can calculate the time it would take for the falcon to travel to the Moon. \(\mathrm{Time} = \frac{386,241,600 \ \mathrm{m}}{97.22 \ \frac{\mathrm{m}}{\mathrm{s}}} = 3,972,299.27 \ \mathrm{s} \) It would take the peregrine falcon approximately 3,972,299.27 seconds to fly to the Moon.
03

Part (c): Calculate the time it takes for light to travel from Earth to the Moon and back again

To find the time it takes for light to travel from Earth to the Moon and back, we can use the formula: time = distance / speed. In this case, we need to double the distance, as light needs to travel to the Moon and back to Earth. The speed of light is given as \(3.00 \times 10^{8} \ \frac{\mathrm{m}}{\mathrm{s}}\). \(\mathrm{Time} = \frac{2 \times 386,241,600 \ \mathrm{m}}{3.00 \times 10^{8} \ \frac{\mathrm{m}}{\mathrm{s}}} = 2.57161 \ \mathrm{s} \) It takes light approximately 2.57 seconds to travel from Earth to the Moon and back again.
04

Part (d): Convert Earth's speed around the Sun to miles per hour

To convert Earth's speed around the Sun from kilometers per second to miles per hour, we can use the conversion factors: 1 km = 0.621371 miles and 1 hour = 3600 seconds. \(29.783 \ \frac{\mathrm{km}}{\mathrm{s}} \times \frac{0.621371 \ \mathrm{mi}}{1 \ \mathrm{km}} \times \frac{3600 \ \mathrm{s}}{1 \ \mathrm{hr}} = 66,616.26 \ \frac{\mathrm{mi}}{\mathrm{hr}} \) Earth travels around the Sun at an average speed of approximately 66,616.26 miles per hour.

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