Question

It’s your birthday, and to celebrate you’re going to make your first bungee jump. You stand on a bridge 100 m above a raging river and attach a 30-m-long bungee cord to your harness. A bungee cord, for practical purposes, is just a long spring, and this cord has a spring constant of 40 N/m. Assume that your mass is 80 kg. After a long hesitation, you dive off the bridge. How far are you above the water when the cord reaches its maximum elongation?

Answer 1

E is denoting the total mechanical energy at the jumping point.

At the point of maximum elongation:

the gravitational potential energy is

                     (-ve sign is due to the downward direction from the jumping point)

the spring's potential energy is

                    

So, the total mechanical energy of the system at maximum elongation is

                          

                                                  

Now applying conservation of energy, we can write

                           

                    or,    

                    or,    

                     or,   

We got two answers. The second answer is due to the fact that:

After elongation, the spring will get compressed back and at 90 m from the ground again the total mechanical energy will become zero. But this case is not required here. So, we will neglect this result.

Hence, at maximum elongation, the boy is 10 m above the water.