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

• ~Sam~
In summary, a 79kg person with a bungee chord of spring constant 40 N/m and length 35 m jumps from a 100m platform. The maximum elongation of the chord occurs when the person is no longer falling and their gravitational potential energy has been fully converted into the spring potential energy. Using the equations F=ma, Ek=1/2mv^2, and Ep=mgh, we can calculate the distance the person is above the water when the chord reaches maximum elongation.
~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.

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.

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.

## 1. How do you calculate the height above water for a person jumping?

To calculate the height above water, you will need to use the equation: h = (1/2)gt^2, where h is the height, g is the acceleration due to gravity (9.8 m/s^2), and t is the time in seconds. Plug in the values of 79kg for the person's weight and 100m for the distance jumped.

## 2. Is the person's weight a factor in determining the height above water?

Yes, the person's weight is a factor in determining the height above water. The equation for calculating height involves the person's weight as one of the variables, along with the acceleration due to gravity and the time in the air.

## 3. Why is the acceleration due to gravity used in this calculation?

The acceleration due to gravity is used because it represents the force that pulls objects towards the center of the Earth. When a person jumps, they are propelled upwards by their own force, but the acceleration due to gravity is constantly acting on them, causing them to eventually fall back to the ground.

## 4. How accurate is this calculation in real life scenarios?

This calculation assumes ideal conditions and does not take into account factors such as air resistance or the person's jumping technique. Therefore, the calculated height may not be completely accurate in real life scenarios, but it can provide a rough estimate.

## 5. Can this equation be used for any distance and weight combination?

Yes, this equation can be used for any distance and weight combination as long as the units are consistent (e.g. meters for distance and kilograms for weight). However, as mentioned before, this calculation may not be completely accurate in real life scenarios due to other factors at play.

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