Give this a try! Let me know if you have questions (I have commented my changes).
% matlab program for solving the bungee jumber problem using Eulers method
g=9.81;
m=80;
cd=0.25;
t0=0;
tend=20;
dt=0.5;
vi=0;
t=t0:dt:tend;
% the analytic solution
vel=sqrt(g*m/cd)*tanh(sqrt(g*cd/m)*t);
% Pre allocate memory for faster run times
v = zeros(11,1);
tt = zeros(11,1);
count = 2;
% Loop through your calculations knowing that initial conditions are zero
for ti = 2:2:20
v(count) = v(count-1) + (g-cd/m*v(count-1).^2).*((ti+2)-ti);
tt(count) = ti;
count = count + 1;
end
% plotting of results
plot(t,vel)
hold on
plot(tt,v','r')
grid
xlabel('time (s)')
ylabel('velocity (m/s)')
title('velocity for the bungee jumber')
legend('analytical','numerical')
