Some background before stating the answer:

The break will occur at the weakest point in the rope. This can be at any
location on the rope. This will leave two ends to be considered separately.
The primary motive force will be the initial elastic deformation of the
rope. At each rope segment contacts it will be drawn to the fixed attachment
point. The accelerating force may be in the magnitude of tons, and the mass
of the rope is likely to be very low in relation to this force. This
suggests that the rope may experience a large acceleration.

There are other forces involved. The inertia of the initial movement of the
rope will be dwarfed the movement induced by the initial tension on the
rope. As the rope contracts, any torsion induced by the lay of the rope will
tend to cause it to twist and coil. Any air movement, or relative air
movement because of boat motions, will further modify the movement of the
rope. Unless the boats are traveling very fast, or in a very high wind, the
initial contraction will be the largest force. As the rope decelerates due
to air friction, the relative air movement may become the final deciding
factor in how the rope moves. Or the stored energy in the flying rope end
may be transfer to any object that it runs into, such as the foolish captain
that tried to tow a boat with a rope that was clearly too small to do the
job.

The final answer:
The remainder of the rope on each end of the break will be drawn towards the
boat to which it is attached.

Mark Browne

"CCred68046" wrote in message
...
Theoretical Situation: Two identical boats. One is towing the other with
a
small diameter (undersized for the job) 30' rope.

Question: When the rope snaps, which way will it go?

Should it snap back towards the boat in tow (the load). Or should it snap
toward the boat pulling the load (the force)?