% Example 9-7: Flight of a model rocket

m=0.05; g=9.81; tEngine=0.15; Force=16; vChute=-20; Dt=0.01;
clear t v h
% n counts the time steps of Dt
n=1;
% Initialize the time, velocity, and altitude variables
t(n)=0; v(n)=0; h(n)=0;

% Segment 1: climbing under power
a1 = (Force-m*g)/m;
% Compute t, v, h at each time step
while t(n) < tEngine
    n = n+1;
    t(n) = t(n-1) + Dt;
    v(n) = a1*t(n);
    h(n) = 0.5*a1*t(n)^2;
end
% Store variables at the end of segment 1
v1=v(n); h1=h(n); t1=t(n);

% Segment 2: no power
% Compute t, v, h at each time step
while v(n) >= vChute
    n = n+1;
    t(n) = t(n-1) + Dt;
    v(n) = v1-g*(t(n)-t1);
    h(n) = h1 + v1*(t(n)-t1) - 0.5*g*(t(n)-t1)^2;
end
% Store variables at the end of segment 2
v2=v(n); h2=h(n); t2=t(n);

% Segment 3: with parachute
% Compute t, v, h at each time step
while h(n) > 0
    n = n+1;
    t(n) = t(n-1) + Dt;
    v(n) = vChute;
    h(n) = h2 + vChute*(t(n)-t2);
end
subplot(1,2,1)
plot(t, h, t2, h2, 'o')
xlabel('Time(s)')
ylabel('Height (m)')
subplot(1,2,2)
plot(t, v, t2, v2, 'o')
xlabel('Time(s)')
ylabel('Velocity (m/s)')