andnowimbroke -- Like others above have mentioned, this will be primarily a flash and trigger problem...not necessarily a shutter speed problem...depending on the specific composition of the photo that you're wanting to capture.
Are you looking for something like Doc Edgerton captured? See:
http://edgerton-digital-collections.org/?s=golf#hee-nc-35006
or something more like a full-bodied golfer hitting the ball at just the right moment:
http://edgerton-digital-collections.org/?s=golf#hee-nc-38111
For your school project, I would recommend studying Edgerton's notebooks that are online at the same site as the links above.
As for making your own photos, there are a lots of circuit designs available to trigger flashes with external events. If you're not up to the soldering and circuit board layout, there are also commercially available units that give a turn-key solution.
See for example:
http://www.cognisys-inc.com
another company that offers some of these triggers is:
http://www.bmumford.com/photo/camctlr.html
Hope this helps!