\documentclass{article}

\usepackage[hyphens]{url}
\usepackage{hyperref}

\begin{document}

First\footnote{This is justified text.  Note that there  is an indent  at the beginning  of the footnote
  which prevents  the  second  line  from  continuing  below  the  footnote number.
  This is justified text.  Note that there  is an indent  at the beginning  of the footnote
  which prevents  the  second  line  from  continuing  below  the  footnote number.}
Second\footnote{This is justified text.  Note that there  is an indent  at the beginning  of the footnote
  which prevents  the  second  line  from  continuing  below  the  footnote number. The new
  paragraph contains a link and should look like this:

  \raggedright
  Source: \url{http://www.example.com/this-is-a-very-long-link-which-words-are-separated-by-hyphens-note-that-the-second-paragraph-contains-the-link-and-should-be-left-justified-like-this}}
Third\footnote{This is justified text.  Note that there  is an indent  at the beginning  of the footnote
  which prevents  the  second  line  from  continuing  below  the  footnote number.
  This is justified text.  Note that there  is an indent  at the beginning  of the footnote
  which prevents  the  second  line  from  continuing  below  the  footnote number.}

\end{document}