Powershell Remove-WebApplication cmdlet will not remove Web Application

I've created a web application within a web site called "MyWebApp" and it's physical path to a folder called "mywebapp". When I use the Powershell v2.0 Remove-WebApplication cmdlet it will not remove the web application. 

My theory is the way Remove-WebApplication works is when it cycles through the IIS directory listing it finds the first name that matches and tries to remove it. 

Type               Name                             Physical Path
----               ----                             -------------
directory          mywebapp                         C:\USNB361VM-USDB12\LEGACY_2455460.0\Support\mywebapp
application        MyWebApp                         C:\USNB361VM-USDB12\LEGACY_2455460.0\Support\mywebapp

In this case it's a directory and not an application "Type". If there really isn't a web application to remove, the cmdlet would throw a "Cannot find path xxxxxx because it does not exist." exception, but in my case no error message was thrown.

There is no "-Type" switch I can use with this cmdlet. How can I zero in on the application type and remove the web application successfully?

Thanks,

Ed