issue using indices...maybe?

Hello everyone,

I have made this code to solve system of equations so when t=0 x should be at target distance.

I shared it with my professor today and she said she thinks it's something to do with the indices...and I am unable to figure it out. The plot should end at the target distance x_t at y=0 and as you can see it hits the target just below y=0. Any help is greatly appriciated.

g = -32.2; % Gravatational constant

%% Please enter angle and target distance. 
a = 45 ; % User input for angle
x_t = 4; % User input target distance
y_o = .5;  % Initial y position at launch 6 in. 

% System of equations to be solved
syms v t 
eqn1 = x_t == v  * cosd (a) *t;
eqn5 = 0 == y_o + v * sind (a) * t + 1/2 *g * t^2;
eqns =[eqn1,eqn5];

% Solve
sol = solve(eqns,v,t);
vS = vpa(sol.v)/1i^2;    
tS = vpa(sol.t)/1i^2;

% Extracting only positive roots for subsequent equations
vpos = vS(vS>=0);
tpos = tS(tS>=0);
% Time step and matrices length
dt=.01;
t_i = 0:dt:tpos;
numt = length(t_i);
y  = zeros(1,numt);
x = zeros(1,numt);

% Simulate the trajectory
vy = vpa(vpos * sind(a));

for i = 2 :numt
    y(1)= y_o;
    vy (i) = vy(i-1) + g * dt;
    x (i) = x (i-1) + vpos * cosd(a) * dt;
    y (i) =  y (i-1) + vy(i) * dt + 1/2 * g * dt.^2;
end


%% Plotting the balls path
  
plot (x,y)
xlim ([0,12.5])
xticks ([0:1:12.5])
ylim auto

hold off
grid on
xlabel ('distance')
ylabel ('Height')
title Projectile Motion

tpos
vpos 

Answer 1

[James Tursa]

You are doing a numeric itegration to generate the plotting points. Numeric integration will build up errors over time, so the fact that your plot doesn't end at 0 exactly is to be expected. You could decrease the step size of your integration, or use a higher order numeric integration scheme, or simply plug some t values into your x and y equations directly to generate the plotting points. E.g., try this and then zoom in on the end point:

t = linspace(0,tpos,1000);
x = vpos  * cosd(a) * t;
y = y_o + vpos * sind(a) * t + 1/2 * g * t.^2;
figure
plot(x,y,'.-')
grid on

[Susan Chestnutt]

Thank you, you are amazing!!!! And don't forget to smile, you deserve it