Capability to work with git project in ProjectExplorer

Now it is not possible to work with git projects effectively bcs. of tracking of changes. Git project with local non-commited changes has prefix for each of those files and also directories recursively. For example:

I have a project ("Project01") in a project explorer which is containing the "src" and "other" folders. Folder "src" could contain other files ("Something"). I create new class in this folder, let's say "MyClass", and this class is not yet commited. Structure would look like this:
"> Project01"
 ---- "> src"
    -------- "> MyClass"
--------     "Something"
---- "other"