Starting from rest, a 64.0-kg person bungee jumps from a tethered hot-air balloo

Question

Starting from rest, a 64.0-kg person bungee jumps from a tethered hot-air balloon 63.0 m above the ground. The bungee cord has negligible mass and unstretched length 23.0 m. One end is tied to the basket of the balloon and the other end to a harness around the person's body. The cord is modeled as a spring that obeys Hooke's law with a spring constant of 87.0 N/m, and the person's body is modeled as a particle. The hot-air balloon does not move.

(a) Express the gravitational potential energy of the person-Earth system as a function of the person's variable height y above the ground. (Use the following as necessary: y and use 9.8 instead of g. Do not include units in your response.)
Ug =

Explanation / Answer

Ug = - GM*m/(y+R) G= grav. constant M= mass of earth m=64kg R= Radius of earth g (9.8) can be written as g= GM/(R^2) => GM =g* R^2 So Ug can also be written in terms of 'g' as Ug= - g* R^2*m/(y+R) => Ug= - (627.2* R^2)/(y+R) where, R= Radius of earth.

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