Monica stepped outside and began to think how fast she is moving even when she is standing still.
Assume that the earth is a sphere with a radius of 3960 miles and Monica is at a latitude of 13∘N.
What is Monica's speed due solely to the rotation of the earth in miles per hour?
looking at a polar cross section
Monica's radius of rotation (r) is
... 3960 mi * sin(90 - 13)
her speed is ... 2 * π * r / 24 hr
To calculate Monica's speed due solely to the rotation of the Earth, we need to know three things:
1. The circumference of the Earth at her latitude.
2. The time it takes for the Earth to complete one rotation.
3. The conversion factor to convert the time into hours.
Let's break it down step by step:
1. Calculating the Circumference of the Earth at Her Latitude:
The circumference of a circle is given by the formula C = 2πr, where C is the circumference and r is the radius. Since Monica's latitude is 13∘N, we need to find the latitude in radians (rad) to use in the formula. To convert degrees to radians, we use the formula: rad = (pi/180) * deg. Therefore, the latitude in radians is (pi/180) * 13. Now, we can calculate the circumference at her latitude: C = 2π * 3960 * (pi/180) * 13.
2. Calculating the Time for One Earth Rotation:
The time it takes for the Earth to complete one rotation is 24 hours, as that is the time it takes for the Earth to make a full rotation.
3. Converting Time to Hours:
As we have the time in hours, there is no need for a conversion factor.
Now, let's plug in the values and calculate Monica's speed:
C = 2π * 3960 * (pi/180) * 13 ≈ 16249 miles (approximately)
Time for one rotation = 24 hours
To find Monica's speed, we divide the circumference by the time for one rotation:
Speed = Circumference / Time
Speed = 16249 miles / 24 hours ≈ 677.08 miles per hour (approximately)
Therefore, Monica's speed, due solely to the rotation of the Earth, is approximately 677.08 miles per hour.