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

[discoron77]

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.

 

[Tide]

How far is that house in Michigan from the axis of the Earth?

 

[discoron77]

It's not given in the problem, I assumed it was half the radius of the earth, but I may be wrong.

 

[Tide]

Um ... that was a hint! :-)

Try a little geometry!

 

[discoron77]

Ok I know I need to use the cosine of 45 in the equation.

 

[discoron77]

Yay! I got it!

 

[Tide]

Way to go!