Smart people! Need help here!

<p>BUNGEE!!!! </p>

<p>Perhaps one of the most unusual and exhilarating recreational activities is the bungee jump. In this 'sport', a series of intertwined elastic cords are attached to a harness, which is either fastened about the person's body or attached to his/her ankles. The other end of the cord typically is attached to a high place like a tower, a bridge, or even a hot air balloon. The person leaps from this structure and falls freely until the bungee cord begins to tighten. The jumper's velocity decreases until he/she momentarily comes to rest, then accelerates upwards. This motion cycle continues for a number of oscillations until the jumper comes to a rest. (The jumper eventually comes to rest due to energy being dissipated as heat in the spring. You may ignore dissipation in this problem). </p>

<p>While the sport of bungee jumping in its present form is quite recent, its origins date back centuries to the ritual of land diving in the Pacific Archipelago. The ritual demonstrated courage and offered injuries to the gods for a plentiful harvest of yams. It wasn't until the late 1970's that this was transformed into a recreational activity. (See The Physics of Bungee Jumping by P.G. Menz in The Physics Teacher, Nov. 1993).</p>

<p>Consider a 90 kg bungee jumper who has a bungee cord strapped to her legs and stands on a platform 50 m above the ground. The bungee cord acts like a giant extensional spring that provides an upward force on becoming taut. In this case the operator has selected a bungee cord with an un-stretched length of 15 m and a spring constant of 100 N/m. </p>

<p>The bungee jumper steps off the platform. At the moment she starts, the jumper has zero velocity. Choosing the ground as your reference point, answer the following questions:</p>

<p>1) What is the maximum potential energy of the bungee jumper?</p>

<p>2) At what height(s) does the bungee jumper have this potential energy?</p>

<p>3) What is the minimum potential energy of the bungee jumper?</p>

<p>4) At what height does she have this potential energy?</p>

<p>5) What is the top speed of the bungee jumper?</p>

<p>6) How close does the bungee jumper approach the ground?</p>

<p>For 1), do I just mgh=(90)(9.8)(50)=44,100 J ?
For 2), is it correct that if I do 0.5(100)d^2 = 44,100? d=29.7 m
I got answers as 50 m and 5.3 m=50-15-29.7
How do u do 3 to 6?</p>

<p>Here my be some clues for you to figure out the answers:
3,4) It is the point of equilibrium (maximum speed, right:) )
5) Get it from the asnwer of 3 :)
6) Just do calculation for the point where speed=0</p>