Using Apache and Tomcat together, delivering JAVA 'files' (servlets, jsp, etc.) doesn't work the way you sketched up. The way you did it there, you can only access the files and they are delivered depending on their mime type.
As a first step you should read up on reverse proxying and in your case the modules
mod_proxy_http and or
mod_proxy_ajp. I don't know what experience level you got, so I simply write up some lines you should adapt:
LoadModule proxy_module /usr/lib/apache2/modules/mod_proxy.so
LoadModule proxy_ajp_module /usr/lib/apache2/modules/mod_proxy_ajp.so
In a standard Linux environment you can install those modules with your package provider and enable them with
a2enmod mod_proxy_ajp. This should also install
mod_proxy as dependency. In that case you drop the LoadModule directives mentioned above.
<Location /> directive is what handles all requests directed to your domain. So
www.project.com delivers the index. There are some more considerations (security when using mod_proxy) and some such, but it should point you in the right direction.