Question

USE MATLAB TO CODE
2. This part is completely independent of analysis performed in #1. A bungee jumper reaches a velocity of 50 m/s when 100 m above the ground. At this point, the bungee cord begins to stretch. The force applied by the bungee cord is proportional to the amount of stretch (Fc=K*stretch). Neglect air drag for the following estimates. a. Determine the minimum spring constant required to stop the 80 kg jumper before hitting the ground. b. Determine the maximum acceleration of the jumper.
USE MATLAB TO CODE

Answer 1

%for part a
initial_velocity = 50; %meters per sec
stopping_distance = 100; %meters
mass = 80; %kg
height = 100; %meters
initial_kinetic_energy = .5*mass*initial_velocity^2;
initial_potential_energy = mass*9.81*height;
initial_total_energy = initial_kinetic_energy+initial_potential_energy;
%final total energy is stored in spring. so we have::
spring_constant = 2*initial_total_energy/(height^2);
disp("spring constant is %s \n",spring_constant)
%for part b:
x = linspace(0,100,10000);

for i=1:10000
acceleration(i) = 9.81-spring_constant*x(i)/mass;
end
[mxa,n] = max(abs(acceleration));

%here mxa is maximum acceleration and x(n) is
%distance at which maximum
%acceleration is attained.
%in this case, max acceleration is attained
%at zero height.