Solving Height Above Water Homework: 79kg Person Jumping 100m

[~Sam~]

Homework Statement

79kg person jumps from a platform that is 100m above the water. He is attached by a bungee chord with sprint constant 40 N/m and length 35 m. Now he jumps off. How far is he above the water now when the chord has reached maximum elongation

Homework Equations

F=ma, Ek= 1/2mv² Ep=mgh...etc

The Attempt at a Solution

I'm kind of stuck.. I know it involves energy, but the maximum elongation of the chord confuses me.

 

[Pengwuino]

All that it means is that the person is no longer falling and is just about to begin moving upward. In other words, the bunjee jumpers gravitational potential energy has been fully converted into the spring potential energy.

 

[kerimek]

I think we need to consider the initial potential energy of the person at the top of the platform and the final potential energy of the person at the maximum elongation of the chord. We can also consider the kinetic energy at the point of maximum elongation. With the given information, we can use the equation Ep=mgh to find the initial potential energy of the person at the top of the platform. Then, we can use the equation Ek=1/2mv^2 to find the kinetic energy at the point of maximum elongation. Finally, we can use the equation Ep=mgh to find the final potential energy at the maximum elongation. By setting these two potential energies equal to each other and solving for h, we can find the height above the water at maximum elongation. However, we also need to consider the spring constant and length of the bungee chord, as they will affect the maximum elongation and therefore the final potential energy. This requires using the equation F=kx, where F is the force, k is the spring constant, and x is the displacement. By setting this force equal to the weight of the person (mg), we can solve for x and then use it to calculate the final potential energy at maximum elongation. Overall, solving this problem involves considering various forms of energy and using equations to find the final height above the water.