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

In summary, to find the linear speed of Santa Fe around the Earth's axis, we can use the formula v = rw, where r is the radius of the circular path and w is the angular velocity. By relating the radius of the Earth, the latitude of Santa Fe, and the radius of the circular path, we can calculate the linear speed to be approximately 1,181.67 mi/hr.
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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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  • #2
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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  • #3
Thank you so much! I figured it out as soon as I saw your diagram.
 

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

1. What is the linear speed of Santa Fe around the earth's axis?

The linear speed of Santa Fe around the earth's axis is approximately 1,037 miles per hour.

2. How is the linear speed of Santa Fe calculated?

The linear speed of Santa Fe is calculated by dividing the circumference of the earth (24,901 miles) by the time it takes for the earth to make one full rotation (24 hours). This results in a linear speed of 1,037 miles per hour.

3. Does Santa Fe's linear speed change throughout the year?

No, Santa Fe's linear speed around the earth's axis remains constant throughout the year as the earth's rotation remains consistent.

4. How does Santa Fe's linear speed compare to other cities around the earth's axis?

Santa Fe's linear speed is the same as any other city located on the same latitude line (35°N). However, cities located closer to the equator have a higher linear speed due to the larger circumference of the earth at the equator.

5. Why is it important to know Santa Fe's linear speed around the earth's axis?

Knowing Santa Fe's linear speed can help us understand the concept of time zones and how they are affected by the earth's rotation. It also allows us to accurately measure and track the movement of objects and phenomena on the earth's surface.

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