Expert: Sherman D. - 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)a. show that at latitude L, Earth's rotational speed in mph is approximately equal to 1038 cos L.
 b. find Earth's rotational speed at the North Pole.

2) Rome, Italy and Boston, Massachusetts, have approximately the same latitude (42°N). A plane flying from Rome due west to Boston is able to "stay with the sun", leaving Rome with the sun overhead and landing in Boston with the sun overhead. How fast is the plane flying? (hint: see part (a) of exercise 1)

Answer
Using 3963mi as the radius of Earth.

C = 2Pi * r
C = 2Pi * 3963
C = 24900.263372352701...
or
C = about 24900 miles

1.)
a.) each latitude is 69 (1/6) miles apart
24900 miles around and 24 hours in a day.
(24900/24) mph = 1037.5mph or 1038mph rounded
as for where the cosL comes in. L° would mean that L° is L° above the 180° mark or 0° mark.

b.) 1038(cos(0)) = 1038(1) = 1038mph

-----------------------------------------------------------

2.)
1038(cos(42)) = 771.38432884mph
or
771mph