% Compute the trajectory of a baseball in flight, with and without air resistance
% and plot results

x = 0.0;      % horizontal position of home plate, meters
y = 1.0;      % height of ball over strike zone
v = 40.0;     % initial speed of ball, meters per second
theta = 76;   % angle of ball off bat, degrees

% initial position and speed of ball
u0 = [x, y, v*cosd(theta), v*sind(theta)]; 

% solve for the first ten seconds of flight
tspan = [0 10];  

% solve the baseball equations numerically
[t, u_withdrag] = ode45(@f_withdrag, tspan, u0);
[t, u_nodrag]   = ode45(@f_nodrag,   tspan, u0);

% get the x,y coordinates from the solutions and plot
figure(1); clf()
x = u_nodrag(:,1);
y = u_nodrag(:,2);
plot(x, y, 'r-')
hold on

x = u_withdrag(:,1);
y = u_withdrag(:,2);
plot(x, y, 'b-')

plot([120, 120], [0, 5.2], 'k-', 'linewidth',2)

legend('no drag', 'with drag', 'outfield fence')

grid on
xlim([-10, 130])
ylim([0, 110])
xlabel('x, meters')
ylabel('y, meters')
title('baseball trajectory')