Any Random, hard, throw able object(s) found around you thrown at someone in desperation.
Like staplers from your desk while your boss is lecturing you about your TPS reports, or your shoe thrown at George Bush for some (Iraqi) reason or another.
Usually these aren't planned to be thrown but used to quickly satisfy the urge to hit someone that is extensively pissing you off.
The Iraqi finally had it with the President of the US, he DESPERATELY looked around for a PROJECTILE;
(hence Desperate Projectile)
removed his shoe and lobbed it at him. The Iraqi not being satisfied with his first throw took off his other shoe and attempted to hit George Bush Again.