stretching and retracting rope

Getting right to it, I'd like to attach a rope to an object that gets thrown. As the object moves away from the origin, the rope should lengthen and as it returns, should shorten. I guess the closest example would be like a yo-yo if also thrown in an arc. I'm avoiding using something like a beam to stretch out since it'll be like a pole instead of something flexible.

I'm sure I'm overthinking it. I bet the current rope in CTF can do this easily but I'm worried about it breaking.