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 between Earth and the Moon in meters is approximately 386,241,600 meters. (b) If the peregrine falcon could fly to the Moon at its maximum speed of 97.22 m/s, it would take approximately 3,970,163.61 seconds to get there.

Step-by-step solution

Convert the distance between Earth and the Moon to meters

First, we need to know the conversion factor between miles and meters. 1 mile is equivalent to 1609.34 meters. So, to convert the distance, 240,000 miles, to meters, we use the following formula: Distance (in meters) = Distance (in miles) * 1609.34 Calculate the distance in meters: Distance (in meters) = 240,000 * 1609.34

Calculate the distance in meters

Now, we can calculate the distance between Earth and the Moon in meters. Distance (in meters) = 240,000 * 1609.34 Distance (in meters) = 386,241,600 m So, the distance between Earth and the Moon is approximately 386,241,600 meters.

Convert peregrine falcon's speed to meters per second

The speed of the falcon is given in km/hr, but we need it in meters per second to make it compatible with our distance calculation. We have the following conversion factors: 1 kilometer = 1,000 meters and 1 hour = 3600 seconds So, we can convert the speed as follows: Speed (m/s) = Speed (km/hr) * (1000 m / 1 km) * (1 hr / 3600 s) Calculate the speed in meters per second: Speed (m/s) = 350 * (1000 / 1) * (1 / 3600)

Calculate the speed in meters per second

Now, we can calculate the speed of the peregrine falcon in meters per second. Speed (m/s) = 350 * (1000 / 1) * (1 / 3600) Speed (m/s) = 350 * (1000) * (1 / 3600) Speed (m/s) ≈ 97.22 m/s So, the peregrine falcon's speed is approximately 97.22 meters per second.

Calculate the time it would take the falcon to reach the Moon

Now, we can calculate the time it would take the falcon to reach the Moon at its maximum speed. To do this, we will use the formula: Time (s) = Distance (m) / Speed (m/s) Calculate the time in seconds: Time (s) = 386,241,600 / 97.22

Find the time in seconds

Finally, we can find out how long it would take the peregrine falcon to reach the Moon at its maximum speed. Time (s) = 386,241,600 / 97.22 Time (s) ≈ 3,970,163.61 seconds Therefore, if the peregrine falcon could fly to the Moon at its maximum speed, it would take approximately 3,970,163.61 seconds to get there.