Hello I often go climbing. When I went with a guide recently he told me that you should be especially carefull when climbing when you only have a small length of rope paid out arguing that because the rope is so short at this point it must take a large shock under a fall. Conversley, if you have a lot of rope paid out, although you will fall further the shock on the rope will be less because the rope has a larger length over which to expand. I think I have solved the problem and just wanted to see if you guys come up with the same answer. Can anyone come up with a quantitative relation to prove the above?