MHB What is the linear speed of Santa Fe around the earth's axis in mi/hr

AI Thread Summary
The discussion focuses on calculating the linear speed of Santa Fe as it rotates around the Earth's axis. Santa Fe's latitude is approximately 33.88 degrees north, and the Earth's radius at the equator is 3960 miles. To find the linear speed, one must determine the radius of Santa Fe's circular path using trigonometric relations involving the Earth's radius and the latitude. The calculation involves using the formula for the circumference of a circle and dividing it by the time it takes for one complete rotation of the Earth, which is 24 hours. The participants successfully engage in the mathematical process to derive the linear speed.
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Santa Fe is approximately 33.88 degrees north of the equator. Given that the Earth's radius at the equator is 3960 mi and the Earth spins around its axis completely in 24 hours, what is the linear speed of Santa Fe around the Earth's axis in mi/hr?

I don't know where to start! Thank you so much!
 
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Consider the following diagram showing a cross-section of the Earth cut with a plane containing the axis of rotation. the vertex of the right triangle containg the angle \(\theta\) is at the center of the Earth. The value \(a\) is the radius of the circular path of Sante Fe as the Earth rotates.

View attachment 8830

Can you find a way to relate the radius of the Earth \(r_E\), the latitude \(\theta=33.88^{\circ}\) and \(a\)?
 

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Thank you so much! I figured it out as soon as I saw your diagram.
 
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