I must find the magnitude of the h step in order to have an x_impact accuracy of 0.1m. I dont understand why when I change my dt my final impact distance changes so drastically when its supposed to approach a final more accurate result.

function Projectile_motion_variation_drag_Magnus  
clear
clc
format long g;
workspace
format compact 
fontSize = 20;

g = 10;                           % acceleration due to gravity in Y
y0 = 0;                             % intial position y
vHit = 50;                          % initial velocity magnitude
wHit = 100;                         % Angular Velocity (rad/s)
Angle = 30;                         % angle of strike

Variation = 0;

if Variation == 1
    v0Max = vHit/10 + vHit;
    v0Min = vHit - vHit/10;
    v0 = randi([v0Min v0Max],1)         %randomly generated v0 
    
    wMin = wHit - wHit/10; 
    wMax = wHit + wHit/10;
    Angular_w = randi([wMin wMax],1)    % randomly generate w

    aMin = Angle - Angle/10;
    aMax = Angle + Angle/10;
    Alpha = randi([aMin aMax],1)        % Angle Alpha hit
else 
    v0 = vHit
    Angular_w = wHit
    Alpha = Angle
end 
    


c = 4.5*10^(-5);                    % Coefficient of drag
r = 21.5*10^(-3);                   % Radius of gold ball
m = 46*10^(-3);                     % Mass of golf ball 
rho_air = 1.2;                      % Density of air 


p = [0 0 0];
dt=0.1; 
t=[0:dt:200];
v = v0;                                    % Velocity Magnitude 

Velx = v(1)*cosd(Alpha);
Vely = v(1)*sind(Alpha)- g*t(1);
Vel(1,:) = [Velx Vely 0] ;                         % Velocity Vector 


FdragX(1) = v(1).*Vel(1).*c;                  % Drag force in X direction
FdragY(1) = v(1).*Vel(2).*c;                 % Drag force in Y direction
AccDragX(1) = -FdragX(1)./ m;                 % F=M*A decceleration due to drag in X
AccDragY(1) = -FdragY(1)./ m;                 % F=M*A decceleration due to drag in Y
AccDrag(1,:) = [AccDragX(1) AccDragY(1) 0] 

u = (pi^2 * rho_air * r^3 * Angular_w);              % Formula for U in z axis
uForce = [0 0 u]                                    % Magnus force in Z
Magnus(1,:) = cross(uForce,Vel(1,:))                % Cross Product of M_force
AccMagnus(1,:) = Magnus(1,:)./m


for i=2:length(t)
    p(i,:) = p(i-1,:) + Vel.*dt + AccDrag.*(dt.^2) + AccMagnus.*(dt.^2);
    
    Vel = Vel + AccDrag.*dt + AccMagnus.*dt;
    v= sqrt(sum((Vel.^2),"all"));
    
    Velx = v*cosd(Alpha);
    Vely = v*sind(Alpha)- g.*t(i);
    Vel = [Velx Vely 0]        
    
    FdragX = v.*Velx*c;                  % Drag force in X direction
    FdragY = v.*Vely*c;                  % Drag force in Y direction
    AccDragX = -FdragX./ m;                 % F=M*A decceleration due to drag in X
    AccDragY = -FdragY./ m;                 % F=M*A decceleration due to drag in Y
    AccDrag = [AccDragX AccDragY 0];
    
    Magnus = cross(uForce,Vel);                % Cross Product of M_force
    AccMagnus = Magnus./m;                     %Acceleration due to magnus force
    if p(i,2)<0
        break
    end
end




fprintf('Velocity with variation' ,v0, 'm/s')

xImpact_no_Drag = (sind(2*Alpha)*(v0^2))/g
p(end,:)
v0
Angular_w 
Alpha

[John D'Errico]

Before you do anything, have you verified that the code is working properly, to predict a reasonable projectile motion? Spend some time to look at that. You are modleing what, a golf ball? Is it predicting anything reasonable? What does the flight do?