The potential energy going into the rope is .959+x meters (x is the distance the rope stretches).
the stored energy in the rope is 1/2 k x^2
set them equal, solve for x.
A 74.2-kg climber is scaling the vertical wall of a mountain. His safety rope is made of a material that, when stretched, behaves like a spring with a spring constant of 1.62 x 103 N/m. He accidentally slips and falls freely for 0.959 m before the rope runs out of slack. How much is the rope stretched when it breaks his fall and momentarily brings him to rest?
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