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Problem: The math behind bungee jumping

This demonstration shows how to use MATLAB to model a simple physics problem faced by a college student.

During spring break, John Smith wants to go bungee jumping. John has to determine which elastic cord is best suited for his weight.

Elastic Cord  Spring Constant A =5 N/m B =40 N/m C =500 N/m
	The air resistance that the bungee jumper faces is R= a1*v - a2*|v|*v Where A1=1 A2=1

The length of the unstretched cord is 30m. The bungee jumpers is 80m above the ground.

To solve this physics problem, we need to:

1. Determine all the forces acting ON the body.
2. Draw a free body diagram.
3. Apply Newton's second law.
4. Solve the equation.

1. Determine the forces acting ON the body.
   Weight (W):
   W = m*g
   m = 90 kg
   g = 10 m/s^2
   Air Resistance (R):
   R=a1*v+a2*|v|*v
   a1=1
   a2=1
   v=dx/dt
   Force from the elastic cord (Fe):
   Fe= k*x if x>0
   0 if x<0
2. Draw the free body diagram.
   
   Please note that we have selected downwards as the positive axis.
3. Apply Newton's second law.
   Net forces=m*a
   W-R-Fe=m*a
   mg-Fe-a1*v+a2*|v|*v=m*a
   where v=dx/dt and a=dv/dt
   
4. Solve the equation.