Problem Statement The differential equation for the velocity of a bungee jumper is different depending on whether the jumper has fallen to a distance where the cord is fully extended and begins to stretch or not. Thus, if the distance fallen is less than the cord length (XL), the jumper is only subject to gravitation and drag forces described in Equation 1. dv =g-sign(v) v2 m Equation 1 Once the cord begins to stretch (x > L), the spring and dampening forces of the cord must also be included as shown in Equation 2. dv =g-sign(v) v2(x-L) - v Equation 2 v = velocity [m/s] t = time [s] g=9.81 [m/s²] sign(x)= function that returns -1 if x is negative, or 1 if x is positive ca second-order drag coefficient [kg/m] m = mass [kg] kcord spring constant [N/m] y cord dampening coefficient [N*s/m] L = cord length [m] Determine the position and velocity of the jumper given the following parameters: L=30 m, m = 68.1 kg, ca = 0.25 kg/m, k = 40 N/m, y = 8 kg/s, t = 0 to 50 s, x (0) = 0, and v (0) = 0. Perform the computation 3 different ways picking one method from each group. Plot and compare the results.