Answer to Question #164873 in Physics for Fern

Question

A mountain climber is attached to a rope. She slips, and after she has fallen 4.5 m, the rope begins to help decelerate her. If the constant deceleration is 5.2g, how many cm will the rope stretch before she stops? (For most real ropes, the deceleration depends on the stretching of the rope.)

Source https://www.physicsforums.com/threads/mountain-climber-how-many-cm-will-the-rope-stretch-before-she-stops.379240/

Answer 1

$$mgh_1=mah_2\\gh_1=5.2gh_2\\4.5=5.2h_2\\h_2=0.865\ m$$