How can I embed a youtube video using variable widths/heights for a dynamic width web page?

I want to set a youtube video to 100% width so that it scales appropriately in a dynamic width column on a web page I am designing.

The problem is that the height doesn't behave like the height of an image. Instead of scaling proportionately, it either collapses (if set to "auto" or left blank) or it scales seemingly random if set to a percentage.

How can I get it to remain proportionate while still dynamic?

With jQuery you could do this:

newwidth = 200; // or worked out dynamically from width of an object after window resize
mov = $('object') // i.e. grab the object, perhaps with another selector too

oldheight = mov.attr('height')
oldwidth =  mov.attr('width')
newheight = newwidth/oldwidth * oldheight

mov.attr('width', newwidth).attr('height', newheight)

EDIT

I've now just created this for a hack I'm working on. In coffeescript because it's so much nicer:

resize_youtube_to_container =  (obj) ->
    newwidth = obj.closest('div').width()  # find the width from parent div
    oldheight = obj.attr('height')
    oldwidth =  obj.attr('width')
    newheight = Math.round(newwidth/oldwidth * oldheight)
    obj.attr('width', newwidth).attr('height', newheight)
    return obj

$(document).ready = ->
    movs = $('object, embed') # need to do both object and embed I think...
    movs.each -> resize_youtube_to_container($(this))

$pattern = "/height=\"[0-9]*\"/";

$string = preg_replace($pattern, "height='120'", $rs['url']);

$pattern = "/width=\"[0-9]*\"/";

$string = preg_replace($pattern, "width='200'", $string);

echo $string;