Solving Tangential Speed at Daytona Beach FL

[ERAUin08]

Hey everybody I have some trouble with this problem.

Homework Statement

At what latitude is the tangential speed of a point due to the Earth's rotation 200 m/s less than is Daytona Beach FL?

The Attempt at a Solution

I honestly don't know where to start. I think I have to do something with measures of triangle angles and lengths of their side. I know I need to give it an honest effort however I don't know where to go. Thank you in advanced.

 

[HallsofIvy]

No, this has nothing at all to do with "measures of triangle angles and the lengths of their sides". It has everything to do with how fast a point moves around a circle. The City of Daytona Beach FL rotates around the axis of the Earth in 24 hours= 24(60)(60)= 86400 seconds. Its "tangential speed" is the circumference of that circle divided by 86400 seconds. you are looking for another point (there are 2 latitudes of points that fit) at which the circumference about which the point moves, also divided by 86400 seconds is that number minus 200:
\frac{C_{Daytona Beach}}{86400}= \frac{C_X}{86400}- 200

No here is where angles and triangles may come into play. If you draw a line from the center of the Earth to Daytona Beach, that line makes an angle a line to the equator equal to the Latitude of Daytona Beach. The line from the center of the Earth to Daytona Beach, the line from Daytona Beach to the axis of the earth, and the axis of the Earth make a right triangle with hypotenuse length equal to the radius of the earth. The radius of the circle Daytona Beach makes around the Earth is radius of the Earth times cos(latitude of Daytona Beach).

 

[ERAUin08]

Ok thank you very much HallsofIvy I really appreciate your help. This class is physics 1 for engineers. I believe I was just lost on what to do because of the wording and experience. Thank you very mcuh