In bungee jumping, it is obviously important to know in advance how far an elastic cord of un-stretched length L will stretch with a given weight attached to its end. In one model for this elongation, the cord is simply considered to be a weak spring with constant k and the person tied to the end of the cord is a point mass m. Air resistance and any pendulum motion of the cord mass system are ignored. Suppose a person jumps from a platform, suspended over water and falls freely until the entire slack cord is extended to length L; denote this point x -0. After the person passes x 0, the cord is stretched an amount x(t). 

(a) Devise a mathematical model for x(t) defined only on the first interval of time 0 s ts T for which x 0. Solve for x(t) and determine the maximum elongation.

 (b) Suppose that L-30 ft, the person weighs 150 lb, and that k 12 lb/ft. How far above the level of the water should the platform be raised so that the person wil elear the water before rebounding upward for the first time? Ignore the height of the person. 

(c) Use the data in part (b) to find the total time it takes the jumper to "reach" the water during the initial jump.