Large web application split into several smaller web apps leads to pathing problems

I'm in the process of splitting a very large web application project into several, more manageable projects.The problem I'm having is with pathing.

Since the new projects used to share a common root (www.mysite.com), they would sometimes refer to each other using a relative path, such as /otherApp/somepage.jsp.

Now since the applications have their own root, if an application tries to refer to the same relative path, the following is produced:

http://ift.tt/1Gn5veE

Is there any way to define an app's root as www.mysite.com while keeping the path to the web app as http://ift.tt/1BKpSGj?

I am currently using Tomcat 7 and developing in Eclipse Java EE Luna