Question

The distance from Earth to the Moon is approximately 240,000 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?

Short answer

(a) The distance from Earth to the Moon in meters is approximately 386,244,480 m. (b) If a peregrine falcon could fly to the Moon at a speed of 350 km/hr, it would take approximately 3,971,720.16 seconds to reach the Moon.

Step-by-step solution

Convert miles to meters

To convert the distance from Earth to the Moon (240,000 miles) to meters, we will use the following conversion factor: 1 mile = 1609.344 meters. So, the distance in meters would be: \( \text{distance in meters} = \text{distance in miles} \times \text{conversion factor} \)

Calculate the distance in meters

Now, we can plug the values and calculate the distance in meters: \( \text{distance in meters} = 240,000 \text{ mi} \times 1609.344 \, \frac{\text{m}}{\text{mi}} = 386244480 \text{ m} \) The distance from Earth to the Moon is approximately 386,244,480 meters.

Calculate the falcon's speed in meters per second

The peregrine falcon's top speed is given as 350 km/hr. We need to convert this to meters per second (m/s) to calculate the time it would take to reach the Moon. \( \text{falcon's speed in m/s} = \text{falcon's speed in km/hr} \times \frac{1000 \, \text{m}}{1 \, \text{km}} \times \frac{1 \, \text{hr}}{3600 \, \text{s}} \)

Calculate the falcon's speed in m/s

Now, plug in the values to calculate the falcon's speed in m/s: \( \text{falcon's speed in m/s} = 350 \, \frac{\text{km}}{\text{hr}} \times \frac{1000 \, \text{m}}{1 \, \text{km}} \times \frac{1 \, \text{hr}}{3600 \, \text{s}} = 97.2222 \, \frac{\text{m}}{\text{s}} \) The peregrine falcon's top speed is approximately 97.22 m/s.

Calculate time in seconds for the falcon to reach the Moon

Finally, to calculate the time it would take for the falcon to travel from Earth to the Moon at its top speed, we can use the following formula: \( \text{time in seconds} = \frac{\text{distance in meters}}{\text{falcon's speed in m/s}} \)

Calculate the time in seconds

Now, plug in the calculated values to find the time in seconds: \( \text{time in seconds} = \frac{386244480 \, \text{m}}{97.2222 \, \frac{\text{m}}{\text{s}}} = 3971720.16 \, \text{s} \) It would take the peregrine falcon approximately 3,971,720.16 seconds to reach the Moon at its top speed.

Key concepts

Distance Measurement Conversion

Understanding how to convert between different units of distance is fundamental in both everyday life and science. In the context of the exercise, the impressive distance from Earth to the Moon was given in miles, a unit common in the United States for measuring long distances. However, globally and scientifically, the metric system prevails, where the meter is the standard unit of length.

To convert from miles to meters, one must know the conversion factor: 1 mile is equivalent to 1609.344 meters. Multiplication of the total miles by this conversion factor gives the distance in meters. Accuracy in these conversions is critical, as even small errors can become significant over astronomical distances.

Converting Miles to Meters

The unit conversion from miles to meters can seem daunting, but it's really just a simple multiplication once you know the conversion factor. It's incredibly vital, for instance, in translating road distances for GPS systems in different countries, or when scientists are sharing data with international teams.

Additional information for the exercise could include a table of conversion factors for units of distance, which serves as a quick reference for students. Encouraging consistent practice is key; as students become more familiar with these conversions, they won't always need a calculator on hand!

Speed Calculation in Physics

In physics, speed is defined as the distance traveled per unit of time and is usually described in terms such as meters per second (m/s) or kilometers per hour (km/hr). The exercise showcases conversion of speed from km/hr to m/s, reinforcing that different scenarios require different units of speed.

The formula for this conversion is built upon the relationship between kilometers and meters, and between hours and seconds. Encouraging students to understand the reasoning behind the conversion, rather than just memorizing the process, aids in long-term retention and application to different problems.

Time Calculation Physics

Time calculation is another essential concept in physics, particularly when discussing motion. It requires an understanding of both speed and distance. When an object travels at a constant speed, the time taken to travel a given distance is found by dividing the distance by the speed.

The exercise asked how long it would take a peregrine falcon to reach the Moon if it could maintain its top speed. By performing this calculation, students practice applying the formula for time and gain a better appreciation for the vast distances in our universe. It also illustrates the concept of time dilation at a very basic level, as realistically, time measurements would become more complex at such high speeds and long distances in space.