How Fast Does Someone Travel Standing on the Equator?

[shawonna23]

As the Earth rotates through one revolution, a person standing on the equator traces out a circular path whose radius is equal to the radius of the Earth (6.38*10^6). What is the average speed of this person in meters per second and miles per hour?

I am really having trouble figuring out what to do for this problem. I know that distance =2*pi*radius. That equals 4.009*10^7. I don't know what else to do

 

[Doc Al]

That equals 4.009*10^7. I don't know what else to do

Don't forget units: in this case, meters. (And you'll need to convert to miles.)

What the definition of average speed? speed = distance/time. Figure out the time: One day equals how many hours? seconds?

 

[wais]

.To solve this problem, we can use the formula for average speed, which is distance divided by time. In this case, the distance is the circumference of the Earth (4.009*10^7 meters) and the time is one day, since the Earth completes one rotation in 24 hours.

So, to find the average speed in meters per second, we can divide the distance by the time:

Average speed = 4.009*10^7 meters / 24 hours

We need to convert the time from hours to seconds, since our distance is in meters and our time needs to be in seconds. One hour is equal to 3600 seconds, so we can multiply the time by 3600 to get it in seconds:

Average speed = 4.009*10^7 meters / (24 hours * 3600 seconds/hour)

Simplifying, we get:

Average speed = 4.009*10^7 meters / 86400 seconds

This comes out to be approximately 463 meters per second.

To find the average speed in miles per hour, we can use the conversion factor of 1 mile = 1609.34 meters. So, we can convert our distance of 4.009*10^7 meters to miles by dividing it by 1609.34:

4.009*10^7 meters / 1609.34 meters/mile = 24902.7 miles

Now, we can divide this distance by the time of 24 hours to get the average speed in miles per hour:

Average speed = 24902.7 miles / 24 hours

This comes out to be approximately 1037 miles per hour.

In summary, the average speed of a person standing on the equator as the Earth rotates is approximately 463 meters per second and 1037 miles per hour.