Physics Questions 2nd Attempt?

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.

Answers should be:

a) 10^3mi/h

b) 10^4mi

c) 10^3mi

So how do I solve the problem while keeping the radius and circumference the same for each equation?

Thanks

Answer 1

I don't think you have enough given information.  I can give you a) assuming NY and Seattle share the same latitude.  It takes 3 hours for the earth to rotate 3000 miles between the cities.  So rate times time equals distance:  rate * 3 hours = 3000 mi or rate = 1000 mi/h.  The reason I brought up latitude, if the cities were NY and Havana, you would have some considerable distance, but little time difference.  

For b), you could get the circumference along the latitude since 3 hours is 1/8 the 24 hour full rotation, the circumference along the latitude would be 8 * 3000 mi = 24000mi . Of course, this is less then the earth's equatorial or great circle circumference.  I don't see where there is sufficient information to solve that.  Same for the radius.  You could get the radius for the latitude circle, which will be less then the earth's radius.  

Sorry I have about 1/3 of a help for you.  I'll be interested in what I'm missing if you get a complete answer!

Answer 2

It is done as follows...

a) 3000miles/3 hrs = 1000miles/hr

b) Earth turns for 24 hrs/day thus Circumference = 1000* 24 = 24,000 miles (not a bad estimate)

c) 2*PI* R = 24,000 thus R = 3819 miles

Your answers are only "order of magnitude".

-Fred