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?

at that latitude r = 3960 * cos(13)

so the speed is 2*pi*r/24 mi/hr

To calculate Monica's speed due solely to the rotation of the Earth, we need to determine the rotational velocity of a point at her latitude. The rotational velocity is the speed at which a point on the Earth's surface moves due to its rotation.

First, we need to find the circumference of the Earth at Monica's latitude. The formula for the circumference of a circle is 2πr, where r is the radius. Since the Earth is not a perfect sphere, but rather an oblate spheroid, the radius is different at each latitude. We can use the formula for the radius at a given latitude, which is:

r = R * cos(latitude)

where R is the radius of the Earth (3960 miles), and latitude is given as 13∘N. In this formula, the latitude is measured in radians, so we need to convert 13∘ to radians by multiplying by π/180:

latitude (in radians) = 13 * π/180

Now, we can substitute these values into the formula to calculate the radius at Monica's latitude:

r = 3960 * cos(13 * π/180)

Next, we can find the circumference of the Earth at Monica's latitude:

circumference = 2 * π * r

Now, we have the distance that a point at Monica's latitude needs to travel within 24 hours due to the rotation of the Earth. Since we want the speed in miles per hour, we divide the circumference by 24:

speed = circumference / 24

By calculating these values, we can determine Monica's speed due solely to the rotation of the Earth.