Matlab 3d projectile secant method with vector - matlab

Question

How can I use the secant method in order to calculate the angle b(between the positive x-axis and negative y-axis) I have to throw a ball for it to land on the x-axis, with these conditions:
the ball is thrown from origo, at a height z=1.4 m, with the and angle a (for the horizontal plane) 30◦, with a speed of 25 m / s. The air resistance coefficient is c = 0.070 and the wind force is 7 m / s at the ground which increases with the height according to: a(z) = 7 + 0.35z.
The motion of the ball is described with the following:
x''=−qx', y''=−q(y'−a(z)), z''=−9.81−qz', q=c*sqrt(x'^2+(y'−a(z))^2+z'^2)
I did a variable substitution (u) and then used RK4 to calculate the ball's motion, however I can't figure out how to use the secant method to find the angle b. The problem is that when I plot with these start and guessing values is that the ball doesn't land on the x-axis:
clear all, close all, clc
a = pi/3; %start angle
c = 0.07; % air resistance coeff.
v0 = 25; %start velocity, 25 m/s
t = 0; %start time
h = 0.1; % 0.1 second step
b = 0
x0 = 0; xPrim = v0*sin(a)*cosd(b);
y0 = 0; yPrim = v0*sin(a)*sind(b);
z0 = 1.4; zPrim = v0*cos(a);
u = [x0 xPrim y0 yPrim z0 zPrim]';
uVek = u';
% Secant method
b0 = 270; % Start guess nr 1
b1 = 360; % Start guess nr 2
f0 = funk (b0);
db = 1;
while abs(db) > 0.5e-8
f1 = funk (b1);
db = f1 * (b1 - b0) / (f1 - f0);
b0 = b1; % Updates b0
f0 = f1; % Updates f0
b1 = b1 - db % new b
end
while u(5) >= 0 && u(3)<=0
f1 = FRK4(t,u);
f2 = FRK4(t+h/2,u+(h/2)*f1);
f3 = FRK4(t+h/2,u+(h/2)*f2);
f4 = FRK4(t+h,u+h*f3);
f = (f1 + 2*f2 + 2*f3 + f4)/6;
u = u + h*f;
uVek = [uVek; u'];
t = t+h;
end
x = uVek(:,1)'; y = uVek(:,3)'; z = uVek(:,5)';
plot3(x,y,z)
xlabel('X');
ylabel('Y');
zlabel('Z');
grid on
where FRK4 is a function:
function uPrim = FRK4(t,u)
c = 0.07;
az = 7+0.35*(u(5));
q = c*sqrt(u(2)^2 +(u(4)- az)^2 + u(6)^2);
uPrim = [u(2) -q*u(2) u(4) -q*(u(4) - az) u(6) -9.81-q*u(6)]';
end
where funk is a function:
function f = funk(b)
a = pi/3
v0 = 25
x0 = 0; xPrim = v0*sin(a)*cosd(b);
y0 = 0; yPrim = v0*sin(a)*sind(b);
z0 = 1.4; zPrim = v0*cos(a);
f = [x0 xPrim y0 yPrim z0 zPrim]';
end