After trying things here and there, the answer was in IIS.
In IIS you can add "applications" inside of your sites.
- Right click the folder in your site where your "second project" is (in my case the folder is "WebService") and select "Add Application..." .
- In alias type the ending path to the URL that you want (in my case my alias would be "v1").
- Point the "Physical path" to the folder where your second project resides (in my case my web service project resides in "WebService/v1/webservice_v1").
- Click OK and you're done.