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?
the radius of the earth at that latitude is
r = 3960 cos13°
so the speed there is 2πr/24 mi/hr
To find Monica's speed due to the rotation of the Earth, we need to consider the Earth's rotation speed and Monica's latitude.
First, we need to determine the rotation speed of the Earth at Monica's latitude. The Earth completes one full rotation in 24 hours, so its rotation speed is 360 degrees per 24 hours, or 15 degrees per hour.
Next, we need to calculate the circumference of the circle traced by Monica's latitude. To do this, we can use the formula:
C = 2πr
where C is the circumference and r is the radius of the Earth.
Substituting the given radius of the Earth (3960 miles), we have:
C = 2π(3960) ≈ 24901.2 miles
Now, to find Monica's speed, we need to determine the distance she travels in 1 hour due to the Earth's rotation. This can be calculated by multiplying the circumference at her latitude by the fraction of the Earth's rotation speed that corresponds to 1 hour:
Speed = (C/24) × (15/360)
Calculating this expression:
Speed = (24901.2/24) × (15/360) ≈ 1036.72 miles per hour
Therefore, Monica's speed due solely to the rotation of the Earth is approximately 1036.72 miles per hour.