FWIW - the video below is actually terrific and worth watching!
<style type="text/css">
.video-container{position: relative; padding-bottom: 56.25%; padding-top: 30px; height: 0; overflow: hidden;}
.video-container iframe, .video-container object, .video-container embed {position: absolute;top: 0;left: 0;width: 100%;height: 100%;}
</style>
<div class="video-container">
<iframe allowfullscreen="" frameborder="0" height="100%" src="https://www.youtube.com/embed/qgP7SGhiHCg?rel=0&showinfo=0" width="100%"></iframe>
</div>
Responsive video in action: