Your problem is in this line:

userInput.nextLine().charAt(0);

The nextLine() method scans everything on the current line and then advances the pointer past that line. So when you call the charAt() method, you are calling it on the next line, which is blank space, and thus an error is occuring.

Instead, change this line to:

userInput.next().charAt(0)

Note, this means other parts of your code will need changed too.

Edit:

Was about to edit my solution, but @Marc-Andre added his answer which covers it, so just cast your eyes over it too.

The problem occurs when line is empty (e.g. ""). Then it doesn't have a character at index 0, hence your error.

To fix, you can check the length of line before you use charAt:

System.out.println(line);
char x;
if (line.length() < 1) {
   System.out.println("next line is empty");
} else {
    x = line.charAt(0);

    while((line.charAt(0)!='/')&&(Character.isWhitespace(x)==false))
    {
       line = inputFile.nextLine();
       if (line.length() < 1) {
          System.out.println("next line is empty");
          break;
       }
       x = line.charAt(0);
       System.out.println(line);
       System.out.println(x);
    }
}