Find an equation v(ϕ) that calculates the rotational speed v of the Earth at latitude ϕ.

The rotational speed v of the Earth at a given latitude ϕ can be calculated using the formula:

v(ϕ) = v0 * cos(ϕ)

where:

• v0 is the rotational speed of the Earth at the equator, approximately 1670 kilometers/hour
• ϕ is the latitude
• cos is the cosine function

This formula is derived from the fact that the speed of rotation varies with the cosine of the latitude. This is because the Earth is a sphere and the speed of rotation is fastest at the equator and slowest at the poles.

Here are the steps to calculate v(ϕ):

1. Convert the latitude ϕ from degrees to radians. This can be done using the formula: ϕ (radians) = ϕ (degrees) * π / 180
2. Calculate the cosine of the latitude in radians: cos(ϕ)
3. Multiply the result by the rotational speed of the Earth at the equator: v(ϕ) = v0 * cos(ϕ)

This will give you the rotational speed of the Earth at the given latitude.