I remember learning a very specific physics lesson. It doesn't quite apply here, but it could have helped. If you're swinging something, you have to let go at ninety degrees from where you want it to fly. It won't fly away the direction that you let go. That's important to know because it could mean the difference between Jason's sling hitting Goliath or hitting one of his friends. That would have totally ruined that Bible story.
Whenever this girl jumped off the swing, it was the wrong time. Honestly, I have no advice on how to land when you're falling like this. If you stick your arms and legs out then you'll end up breaking them. If you don't stick your arms and legs out then you end up breaking your face. Some situations are no-win scenarios.