Problem 1:

Due with homework assignment of January 26.

Alice and Bob are located at the same point on the surface of the Earth, which I assume now is located on the equator.  Alice walks 50 miles straight west, while Bob walks 50 miles straight north.  Then, Alice turns exactly 90 degrees to her right and walks straight ahead for 50 miles, while Bob turns exactly 90 degrees to his left and walks straight ahead for 50 miles.  Do they end up at the same point?  Why or why not?


It is important in this problem to specify what I mean by straight, which is the following.  In this problem, I declare a path to be straight if for any two
points on the path, the quickest way to walk between these two points on the surface of the earth is to follow that path.  Of course, we are going to idealize things in this problem, so you can and should assume that there are no hills or obstacles of any sort (like water, zombies, etc.) along either of their paths.