Charlie:

oddy wrote:...my description is taken from what my friend typed into facebook chat so is probably not a faithful replica.

It is not the original wording, as I said a few posts ago.

Sorry for all the confusion, mostly it's because of my [friends] bad transcription.

pizzazz wrote:Huh? Presumably, since she is hanging from a point above, "20 degrees to the horizontal" seems to me like it should mean "20 degrees below the line perpendicular to the cliff/parallel to the ground" and so 42 degrees would be farther down, not up.

Charlie! wrote:For most interpretations, I think your answer (42 degrees) is physically impossible, since the starting point (and max if she starts at rest) is 20 degrees.

The overall acceleration is in a direction 20 degrees below the horizontal, but the rope itself is at a greater angle. Your are right in your understanding of "20 degrees to the horizontal", pizzazz, but the idea is that the person is standing with their feet against the wall, like an abseiler. They slip and equilibrium is broken, and they accelerate in that direction. The angle we are trying to find is the angle that the rope makes with the (presumed) vertical cliff at the instant that they slip.

All the confusion seems to stem from the "begins to move" statement. I understand that it would describe circles (I've done M3 in which vertical circles do feature), but as it is M1 they do not know anything about circular motion, it could not be that. In vertical circles there is a radial acceleration [math]v^2/r=rw^2[/math] and a transverse acceleration [math]gsin (theta)[/math] In this particular instant, the

resultant of the two accelerations is at 20 degrees below the horizontal. So the overall acceleration being 20 degrees below the horizontal

doesn't imply that the rope is at 20 degrees.

However, if the the

transverse acceleration were at 20 degrees to the horizontal, the rope

would be at 20 degrees to the vertical. The transverse acceleration is at 42.6 degrees below the horizontal, the radial acceleration 'pulls it up', i.e. they all form a nice vector triangle, with the resultant at 20 degrees below the horizontal.