I developed a dynamic web project in Eclipse. I can access the app through my browser using the following URL:
http://localhost:8080/MyDynamicWebApp
I just wanted to add that if you don't want your application name in the root context at all, you and just put "/" (no quotes, just the forward slash) in the Eclipse --> Web Project Settings --> Context Root entry
That will deploy the webapp to just http://localhost:8080/
Of course, this will cause problems with other webapps you try to run on the server, so heads up with that.
Took me forever to piece that together... so even though this post is 8 years old, hopefully this will still help someone!