# Person rotating about Earth

1. Sep 23, 2009

### SoxFan

1. The problem statement, all variables and given/known data
A woman 1.6 m tall stands upright at latitude 50 degrees for 24 hours.
a) How much farther does the top of her head move than the soles of her feet over this interval?
b) How much greater is the acceleration of the top of her head than the acceleration of the soles of her feet?

2. Relevant equations
I know exactly what the question is asking for, but I do not know how to incorporate the angle in the problem.

3. The attempt at a solution
I honestly do not know where to start, as I'm not sure how to use 50 degrees in my work.

My attempt was to use the equation deltaT = 2(theta)r/v. And solving for v, I'd get the velocity of her feet, using R = radius of the earth. Multiplying that in the number of seconds in a day would give meters. I would then do the same for the top of her head, but add 1.6 m to the radius of the earth. Then compare the two distances and the difference would be how much further her head traveled.

For the record, I doubt that's anywhere close to how you do this problem, but that was my best shot.

Any help would be appreciated.

Last edited: Sep 23, 2009
2. Sep 23, 2009

### willem2

A person on the earth rotates in a circle around an axis going through the poles. Only on the equator is the radius of this circle the same as the earths radius.
draw a triangle with as sides:
-the rotation axis of the earth.
-A line from the center of the earth to the woman
-a line perpendicular to the rotation axis through the woman.
use this to find out the radius of the circle that the woman's feet rotate in.

then found out how much further her head is from the earths rotation axis.