You are a thief and you want to lower yourself from the rooftop to a second floor window, which is at a distance H=12m below the tip of the roof. You want to use a nylon rope, which has a failure stress of 400MPa and a Young's modulus of 1GPa.
If your mass is 102kg, and the acceleration of gravity is g=9.8m/s2, what diameter rope, Dmin (in mm), should you choose if you want a safety factor of 2 against failure?
With this diameter rope, at what distance (in m) should you tie the rope to the tip of the roof and to your waist, (what unloaded length, L0 of rope should you have) so that when you dangle from the roof the length of the rope becomes equal to H and you are exactly in front of the window?