Ninja Rope

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He wants to be able to fire a rope, which latches onto a surface, and allows you to pull in slack or let ot slack as you swing. And of course, he wants you to accelerate as you swing.

You get the acceleration from swinging from gravity. Gravity pulls you downward, and you fall faster and faster.

But the rope constrains you. It keeps you a certain distance from the point at which it's attached.

And of course you need momentum. Gravity doesn't just pull you down at a constant speed, it increases your speed by X amount each frame.

Unfortunately I never wrote any physics which works with stick constraints like this so I can't help ya out more than that. Look up "stick constraint" on google or gamasutra and you might find what you need.