Calculate Speed of House in Michigan Due to Earth's Rotation

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Homework Help Overview

The discussion revolves around calculating the speed of a house in Michigan due to the Earth's rotation, specifically at a latitude of 45 degrees. Participants are tasked with determining this speed in miles per hour while considering the radius of the Earth.

Discussion Character

  • Exploratory, Assumption checking, Mathematical reasoning

Approaches and Questions Raised

  • Participants explore the necessary calculations, with one questioning the distance from the house to the Earth's axis. Another participant suggests using geometry and trigonometric functions, specifically the cosine of 45 degrees, in their approach.

Discussion Status

The discussion is active, with participants sharing insights and hints. There is a sense of progress as one participant indicates they have arrived at a solution, although no details are provided.

Contextual Notes

There is uncertainty regarding the distance from the house to the Earth's axis, as it is not specified in the problem. One participant assumes it to be half the radius of the Earth, but this assumption is questioned.

discoron77
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I've been stuck on this problem, and wondering what I need to do to figure it out.

Michigan is a latitude 45 degrees, i.e., half-way between the equator and the north pole. Calculate the speed of a house in Michigan, due to the rotation of the earth. (This speed is for motion relative to the fixed stars, but ignoring the motion of the Earth around the sun.) (The radius of the Earth is 3963 miles.) Express the result in miles per hour.

Any help would be appreciated.
 
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How far is that house in Michigan from the axis of the Earth?
 
It's not given in the problem, I assumed it was half the radius of the earth, but I may be wrong.
 
Um ... that was a hint! :-)

Try a little geometry!
 
Ok I know I need to use the cosine of 45 in the equation.
 
Yay! I got it!
 
Way to go!
 

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