Christian Ethics - Part 1 - The Train

I'm about to start a module at uni on Christian Ethics. In preparation for this I have some questions set to discuss with friends and family. So I would much appreciate your thoughts on the following!

1. A runaway carriage is hurtling down a track where it will kill five people. You are standing on a bridge above the track and, aware of the imminent disaster, you decide to jump on the track to block the carriage. Although you will die, the five people will be saved. But just before your leap, you realise that you are too light to stop the carriage. Next to you, a fat man is standing on the very edge of the bridge. He would certainly stop the carriage, although he would undoubtedly die from the impact. A small nudge and he would fall right onto the track below. No one would ever know. Should you push him? Why?