When dealing with things like this, I go by what little logic and physics I know... and ignore the people who constantly shout "Well, IT'LL NEVER HAPPEN. Time travel is impossible. I'm so damn close-minded I can't think beyond what I've heard" (I really dislike those people... but I've only seen one of them and he's on Zenhex)
Anyway.
This "loop" has no forced start (i.e. someone didn't tell you to stop yourself from being killed, which then wouldn't happen so they couldn't tell you), so I'd say that if, for some reason, you spontaniously traveled back in time a few minutes and through space a relative short distance... there's nothing to stop you throwing the rock. And I don't see any reason for a person to not be in two different places at the same time (since the two of you won't be in the same space-time).
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