Centripetal acceleration along a latitude of Earth

[mncyapntsi]

Homework Statement

An elephant is located on Earth’s surface at a latitude lambda Calculate the centripetal acceleration of the elephant resulting from the rotation of Earth around its polar axis. Express your answer in terms of lambda, the radius RE of Earth, and time T for one rotation of Earth. Compare your answer with g for lambda = 40º.

Relevant Equations

ac = v^2/r

Hello,
I am attempting to correctly solve this problem, however I end up with an equation that is slightly different as the one provided in the textbook solution.
For question (a) I get the same thing, just instead of cos, I have cos^2 and I can't figure out where I went wrong. My process was to go from v = d/t where d = REcos(lambda)pi2, and t = T. Then ac=v^2/r=[(REcos^2(lambda)4pi^2] / T^2.
Any help would be much appreciated!
Thanks!

 

[Chestermiller]

Your rendering of your equations is a mess. I can't figure them out. Please use LaTex.

 

[gmax137]

instead of cos, I have cos^2

maybe you forgot to divide by r?

Your rendering of your equations is a mess. I can't figure them out. Please use LaTex.

Please follow Chet's advice. Help finding an algebra mistake is a big ask when the equations are written out as shown in your post.

 

[haruspex]

Then $a_c=v^2/r=[(RE\cos^2(\lambda)4\pi^2] / T^2$.

What did you substitute for r there? What is the radius of the elephant's rotation?

To convert to latex, all I did was insert \ in front of cos, lambda and pi; insert _ in ac; and put a double hash ($\#\$#) fore and aft.