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 (6.38 106 m). What is the average speed of this person in meters per second?
speed= 2PIr/time r is rad earth, time is one day (in seconds).
To find the average speed of a person standing on the equator as the Earth rotates through one revolution, we can use the formula for average speed:
Average speed = Total distance / Total time.
The total distance covered by the person is the circumference of the circular path traced out, which is equal to 2π times the radius of the Earth. We are given that the radius of the Earth is 6.38 * 10^6 meters, so the total distance is:
Total distance = 2π * 6.38 * 10^6 meters.
The total time it takes for the Earth to complete one revolution is 24 hours, or 24 * 60 * 60 seconds. So the total time is:
Total time = 24 * 60 * 60 seconds.
Now we can substitute these values into the formula for average speed:
Average speed = (2π * 6.38 * 10^6 meters) / (24 * 60 * 60 seconds).
Calculating this expression will give us the average speed in meters per second.
To calculate the average speed of a person standing on the equator as the Earth rotates, we need to determine the distance traveled by the person in one revolution and the time it takes for one revolution.
First, let's calculate the distance traveled by the person. The distance traveled in one revolution is equal to the circumference of the circular path traced out by the person standing on the equator.
The circumference of a circle can be calculated using the formula C = 2πr, where C is the circumference and r is the radius of the circle. In this case, the radius of the circular path is equal to the radius of the Earth, which is given as 6.38 * 10^6 meters.
So, the distance traveled by the person in one revolution is:
C = 2π * 6.38 * 10^6 = 2 * 3.14 * 6.38 * 10^6 = 40.15 * 10^6 meters.
Next, we need to determine the time it takes for one revolution. The Earth completes one revolution in approximately 24 hours or 86,400 seconds.
Now, we can calculate the average speed using the formula: average speed = distance / time.
Average speed = 40.15 * 10^6 meters / 86,400 seconds.
Simplifying the expression:
Average speed = 464.16 meters per second.
Therefore, the average speed of a person standing on the equator as the Earth rotates through one revolution is approximately 464.16 meters per second.