In the book Fellowship of the Ring, when the Fellowship is camped at Parth Galen above the Falls of Rauros, Frodo walks off alone to decide what to do next. Boromir slips off after Frodo and tries to steal the Ring. Frodo puts the Ring on and disappears; Boromir returns to the rest of the group and says that Frodo vanished. Aragorn suspects that Boromir isn't telling the whole story, but doesn't know exactly what Boromir is leaving out (though he may have a pretty good idea of what really happened).
The group immediately splits up without any attempt to coordinate their efforts, and everyone goes running off in different directions. Gimli and Legolas run one way; Sam another, Merry and Pippin go off in a third direction, and finally, Aragorn steps up and tries to impose some semblance of order to the search, instructing Boromir to go after Merry and Pippin while he chases Sam. He actually overtakes Samwise, and tells Sam to follow him, but Sam realizes that Frodo plans to leave the Fellowship on his own, and runs after Frodo.
As a result of this disorderly dash into the woods, Boromir is killed (but after all, the whole mess is his fault), Merry and Pippin are captured, Legolas runs out of arrows, and Sam and Frodo slip away alone. This is a catastrophic outcome, especially for Boromir (and later, for Minas Tirith, whose defense is ineptly overseen by Boromir's father, now mad with grief).
Why did the Fellowship split up and sprint off in different directions? The hobbits can be forgiven for panicking, since they don't know any better, but Gimli is a hardened warrior and Legolas is a fairly experienced warrior who is also an elf, and therefore supposedly very wise. Their behavior seems especially out of character and short sighted.
The only explanation I can think of is that the fact that Frodo used the Ring has something to do with it - specifically that the Ring itself made everyone freak out, but I have no evidence to support this theory.
Is there some canonical explanation for the Fellowship's surprising, ill-advised, and reckless behavior in this situation?
I'm hoping for an answer other than "They were worried about Frodo", which seems to be a weak argument in my opinion - they didn't freak out this much when Frodo was stabbed in Moria, or near Weathertop, or at any other time - even when Gandalf fell. However, I will accept whichever answer is most convincing