Physics- Order of Magnitude Question?

Question

New York is roughly 3000 miles from Seattle. When it is 10:00 A.M. in Seattle, it is 1:00 P.M. in New York. Using this information, estimate (a) the rotational speed of the surface of Earth, (b) the circumference of Earth, and (c) the radius of Earth.

Answer 1

being a word problem you have to take it as is.  that said, there is not enough information to solve anything.  you would need to know the latitude of both cities which is not given.

the best you can figure, assuming we have a 24 hour day (again, not given) would be that NY and Seattle are 1/8th (3/24ths) of the earth circumference separation between the them.  that assumes that NYC and Seattle are at the same latitude.  but again, doubt i'd assume that.

Answer 2

Total time difference if you go around the globe is ~24 hours. So if the time difference is ~ 3 hours then the distance must be (3/24) = 1/8 th the circumference of the earth. Thus, we get answers in this order:

(b) circumference of the earth = 8 * 3000 miles = 24000 miles

(c) circumference of a circle drawn around the earth = 2*pi*radius

that means that radius = (24000 miles) / (2 * pi) = 3820 miles

(a) the earth covers 3000 miles from seattle to new york in 3 hours so its rotationals speed is = 3000 miles/3 hours = 1000 miles /hour

Answer 3

Rotational speed = miles per hour.  You have 3000 miles to cover in 3 hours, so rotational speed is 1000 miles per hour.

The earth rotates every 24 hours.  If it's moving at 1000 miles per hour, then the earth must be 24,000 miles in circumference.

If c = 24,000 miles, then using c = pi*2r we can calculate the radius of the earth to be c/(2*pi) = 3820 miles.

(Note:  the accepted value of the earth's radius is 6.37 x 10^6 m.  If you convert the 3820 miles to meters it matches.  Yay.)