Expert: Bobby Soltani - 1/15/2005

Question
these are physics type problems that are related to sine and cosine.

*use this info to solve problems: use 3963 mi. for the radius of Earth.

1) Earth's rotational speed at the equator is found by dividing the circumference of the equator by 24 hours: 24,902 mi. / 24 h. ~ 1038 mi/h
What is Earth's rotational speed at:
a) Bangor, Maine (latitude 45°N) and
b) Esquina, Argentina (latitude 30°S)?

Answer
Hi Amy,

a) latitude 45 degrees
45 degrees is halfway from the equator to the North Pole, so Bangor is 3963/2 = 1981.5 miles north of the equator.
1.  Draw a circle representing the Earth
2.  Draw a line across the circle to represent the equator
3.  Draw a line across the circle halfway between the equator and the north pole.  This is the radius of the earth at Bangor.
4.  Draw a line connecting the two parallel lines starting at the center of the Earth.  This distance is 1981.5 miles calculated above.
5.  Draw a line from the center of the earth to the edge of the circle at the radius of Bangor.  The length. of this line is the radius of the Earth (3963 miles).

Now we have created a right triangle with one side that is the radius of the Earth at Bangor, one side that is the distance from the center of the Earth North to Bangor, and the hypotenuse which is the radius of the Earth.  We can use Pythagorean's theorem.

r^2 + 1981.5^2 = 3963^2
r = 3432

So, the radius at Bangor is 3432 miles.  The circumference is C = 2*pi*3432 = 21564 miles.

The speed is C / 24 h = 898.5 miles / hour

b) do the same steps except Esquina is only 1/3 of the distance between the equator and the south pole (30 degrees / 90 degrees = 1/3).  So, the distance is 3963/3 = 1321 miles instead of 1981.5.

Let me know if you have questions.

Bobby