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?
To find Monica's speed due solely to the rotation of the Earth, we need to consider the rotation of the Earth at her particular latitude.
First, let's calculate 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 of the circle.
Given that the radius of the Earth is 3960 miles, we can calculate the circumference at her latitude as follows:
C = 2π * 3960 miles
Next, we need to find the time it takes for the Earth to complete one rotation. The Earth rotates once every 24 hours, which is equivalent to 24 * 60 = 1440 minutes or 1440 * 60 = 86400 seconds.
To calculate Monica's speed due to the rotation of the Earth, we divide the circumference of the Earth (at her latitude) by the time it takes for one rotation:
Speed = Circumference / Time
Speed = (2π * 3960 miles) / 86400 seconds
This will give us Monica's speed in miles per second. To convert this to miles per hour, we multiply Monica's speed by the number of seconds in an hour (3600 seconds):
Speed = (2π * 3960 miles / 86400 seconds) * 3600 seconds
Finally, we can simplify the equation and compute the value to find Monica's speed due to the rotation of the Earth in miles per hour.