Fark linked up this graphic example of what a bird strike looks like from the pilot's point of view. Video is not gross, but is pretty intense. It seemed to take forever the first time I watched it, but from slightly before the strike to the airplane hitting the ground took almost exactly 60 seconds. Sounds like everyone (well, every person) got out Ok. In the comments, the story is claimed to be as follows:

I visit your site quite regularly, but I've never written in till now. The jet in question is a CT-155 Hawk. It is a jet trainer built by British Aerospace Systems and flewn by the Canadian Air Force.(CT-155 is the Canadian designation. The British designation is BAE 115 Hawk, or something like that.) The accident happened about 2 years ago in Moose Jaw, Saskatechewan, where a lot of the pilot training for the Canadian Air Force is done. I just completed pilot training there myself, although I didn't fly the Hawk. Anyway, as you can see, they had a bird strike shortly after take-off. They were doing about 230 knots, and at 200 feet when they sucked in the bird. The one and only engine flamed out almost immediately. There was a student and instructor in the airplane at the time. The instructor immediately took control and attempted to turn around in order to carry out a forced landing. However, they didn't have enough altitude and decided to eject. They were at about 800 feet, 150 knots when the ejected. Both pilots survived. The student had virtually no injuries. The instructor severely injured his spine and broke his leg. The student returned to flying almost immediately. I am unsure if the instructor is back flying, but as of about 7 or 8 months ago, he was not.

Here is a link to a site with several pictures of the Hawk, as well as more info. I'd be happy to answer anymore questions you may have.

Cheers,
Mike G.
Pilot, Canadian Air Force

Which nicely explains why they weren't able to just power away on a single motor. An F-15 would probably get away with it. A trainer, not so much.