Circular motion of plane flying at 40.1 degrees [CAPA Question]

[ghostanime2001]

Homework Statement

How fast must a plane fly at a latitude of 40.1° so that the sun stands still relative to the passengers?

Note: I am using Randall D. Knight's Physics for Scientists and Engineers 2nd edition because that is the required book for this course. I am told to use the radius of the Earth given inside this textbook. The radius is 6.18E6 m.

Also I know that the Earth moves 1 period (T) in 24 hours = 86,400 seconds

Homework Equations

$$v=2 \pi r/T$$

The Attempt at a Solution

$$v = \frac{2 \pi rcos 40.1}{86400}$$

$$= 343.77 m/s$$

However the answer is 355 m/s (after the due date for CAPA) what am I doing wrong? Also, I am having a very difficult time understanding "...the sun stands still relative to the passengers"

 

[tiny-tim]

hi ghostanime2001!

I am told to use the radius of the Earth given inside this textbook. The radius is 6.18E6 m.

very strange

http://en.wikipedia.org/wiki/Earth" reckons the mean radius is about 6370 km, which gives the correct result

 

[ghostanime2001]

Okay maybe I haven't told you everything! :(

Maybe the radius of the Earth inside my book is wrong. But in the first question on CAPA there is a question that goes like this: "The Earth's radius is about 3840 miles. Kampala, the capital of Uganda, and Singapore are both nearly on the equator. The distance between them is 5150 miles... blah blah"

So I suppose i will take the radius given in that first question and convert it to meteres. Which I did and it turns out to be (using factor label method) = 6,179,880.96 meters

I did the exact same thing with this and got another answer which is nowhere near 355 m/s... Sighhhhhh I don't understand am I doing the question wrong?

The answer I got is 343.77 m/s :(

 

[ghostanime2001]

OMG! you (or I) would believe this... the value 6.18E6 is not from the textbook. This value is the one i got when I converted from miles to meters from the first question on my CAPA assignment. I re-checked the value in my textbook and it says 6.37E6 m. Here is proof if you don't believe me. Click on the attachment below titled "Vol1.bmp"

I am really sorry for the misunderstanding. But thanks anyway for a "silent hint" :P
The answer I get now is 354.34 m/s. I guess that is close to 355 m/s ?