What is the average speed at a given latitude due to Earth's rotation?

[ScienceGirl90]

Homework Statement

Any person on the Earth is carried in a cirular path as the Earth rotates on axis. The Earth revolves once in a day. At a latitude of Φ, the distance to the axis of rotation is R = R_Earthcos(Φ). If Anytown's latitude is 48.8 degrees and the Earth's radius is 6378 km, what is your average speed at Anytown's latitude due to the Earth's rotation? Express your answer in m/s.

Homework Equations

R = R_Earthcos(Φ)
velocity=distance/time

The Attempt at a Solution

I tried first to switch the Earth's radius from kilometers into meters to get it into the right format of m/s. I tried then to put it into the equation for the distance to the axis of rotation...R=(6378000)*cos(48.8) and then divide that number by the number of seconds in a day (86400) but I don't get the right answer. I think I'm just confusing myself more than anything else. Any help would be appreciated!

 

[jhae2.718]

$$R_E\cos(\phi)$$ is not the total distance traveled. It is just the distance to the axis of rotation. You need to come up with an expression for the total distance traveled in a day at that latitude.

 

[ScienceGirl90]

Oh I see. I guess I just don't understand how to come up with an expression with the information provided or how to use the equation given properly.

 

[jhae2.718]

If you have a radius, and assume the Earth is circular in cross section, what is the distance around it? Think geometry.

 

[ScienceGirl90]

Ok. So then I need to find the circumference to find the total distance traveled?

C=pi*r²
C=pi*(6378)²= 127796483.1

 

[jhae2.718]

The circumference is $$C=2\pi r$$. What you have is area.