Mountain Climbing

I went on pre-orientation hiking trip before freshmen year where we hiked two high peak mountains that we had passed through. There was one high peak mountain that we passed but didn't climb called Wallface mountain. One does not usually reach the top of this mountain by hiking. People often use rock climbing techniques to reach the top of the mountain. When people rock climb, they often use nylon ropes to attach themselves to the steep cliff they need to surmount. There is a specific reason climbers use nylon ropes, and that is to protect themselves in case they fall. 
If a rock climber begins to fall, his/her momentum will be halted because of the rope. Nylons ability to stretch past its equilibrium point when there is a falling mass will result in a force being applied to the climber that will occur over a longer period of time. Extending the amount of time that the climbers momentum is stopped will reduce the force exerted on the climber . 
When the climber falls, he/she falls with constant acceleration with a mass of about 75 kg. If the nylon rope is 5 meters long, then the climber will accelerate for 5 meters before the rope stretched past its equilibrium point. The climbers weight is the force applied, and if the nylon is 2.5cm in diameter, is 5m long, and its Young's Modulus is about 3x10^9 N/m^2, then you can calculate how much the nylon rope will stretch by the equation F = (E ΔL A)/ Lo.  The climbers final velocity after 5m is given by the equation vf=sqrt(2ad). The climbers momentum at that same point is given by mvf. Past this point, the climber still accelerates, but at a smaller rate. The point where the acceleration  is zero s when the force of tension of the rope equals the mg of the climber, and is the point where the nylon is fully stretched (its change in L). If F= change in momentum/change in time, then if nylon stretched more than other material, then the climber will fall longer and have a smaller force acting on him, making the fall safer. 

sources: http://www.physicsclassroom.com/class/momentum/Lesson-1/Real-World-Applications
http://www.bestech.com.au/wp-content/uploads/Modulus-of-Elasticity.pdf