A person wants to participate in a bunjee jump. One end of an elastic band 10m long with a spring constant of 50N/m will be attatched to a basket on a crane and the other end to the waist of the person with a mass of 86kg. The person will step off the edge of the basket to be slowed and brought back by the elastic band before hitting the ground (hopefully 2m above) How high should the crane be? (hint: conservation of energy).

Question

A person wants to participate in a bunjee jump. One end of an elastic band 10m long with a spring constant of 50N/m will be attatched to a basket on a crane and the other end to the waist of the person with a mass of 86kg. The person will step off the edge of the basket to be slowed and brought back by the elastic band before hitting the ground (hopefully 2m above) How high should the crane be? (hint: conservation of energy).

I know I use this equation but I am confused on how to solve for h when there is h on both side of the equation?
MgH = (1/2)*k*(H-2-10)^2 + Mg*2

Answer 1

expand the square on the right, gather terms, put it in the standard quadratic form, and use the quadratic formula.

Answer 2

I get 54.5 when I caculate the answer

Answer 3

To solve for the height of the crane, we can make use of the principle of conservation of energy. The equation you mentioned is correct:

MgH = (1/2)*k*(H-2-10)^2 + Mg*2

Let's break down the equation:

MgH represents the potential energy of the person at height H (with respect to the chosen reference point).

(1/2)*k*(H-2-10)^2 represents the elastic potential energy stored in the elastic band when the person is brought back after being slowed down. Here, k is the spring constant, and (H-2-10) is the amount by which the elastic band is stretched (H-2 is the distance from the ground to the point where the person is fully stretched, and 10 is the initial length of the elastic band).

Mg*2 represents the potential energy of the person when 2m above the ground.

To solve for H, start by simplifying the equation:

MgH = (1/2)*k*(H-12)^2 + Mg*2

Next, expand the squared term:

MgH = (1/2)*k*(H^2 - 24H + 144) + Mg*2

Multiply through by 2 to eliminate the fraction:

2MgH = k*(H^2 - 24H + 144) + 2Mg*2

Now, distribute k:

2MgH = kH^2 - 24kH + 144k + 4Mg

Rearrange the equation so that all the terms are on one side:

kH^2 - 24kH + 144k + 4Mg - 2MgH = 0

This is a quadratic equation in H. To solve for H, you can substitute the known values for k, Mg, and solve for H using either the quadratic formula or factoring technique.

Please provide the values of k, Mg, and solve for H using quadratic formula or factoring if needed.