Forward, central, backward difference

I am struggling making this code work. I have to show For the initial velocity of 25 m/s and kick angle of 40 plot the trajectory of the ball. The finite difference method (forward, backward, and central finite difference)need to be used to approximate the derivative of an equation

Estimate the value of the first derivative using the forward, backward and central finite difference

Plot the approximated values from each method on the same plot once along horizontal direction x and once along vertical direction y for the kick angle of 40. Label the plot and discuss the error. code is:

theta0=40; v0=25; deltat=0.01; [x,y,t]=projectile_simple(v0, theta0, deltat);

%%finite diference %forward Vx_f=zeros(1,length(x)); Vy_f=zeros(1,length(x));

for jj=1:length(x)-1 Vx_f(jj)=(x(jj+1)-x(jj))/deltat; Vy_f(jj)=(y(jj+1)-y(jj))/deltat; end

%need correction for last index Vx_f(end)=Vx_f(end-1); Vy_f(end)=Vy_f(end-1); figure hold on plot(t,Vy_f)

%% % %backward Vx_b=zeros(1,length(x)); Vy_b=zeros(1,length(x));

for k=2:length(x) Vx_b(k)=(x(k-1)-x(k))/-deltat; Vy_b(k)=(y(k-1)-y(k))/-deltat; end

%need correction for last index Vx_b(1)=Vx_b(2); Vy_b(1)=Vy_b(2); %deltat=x(2)-x(1);

plot(t,Vy_b) % %% %central Vx_c=zeros(1,length(x)); Vy_c=zeros(1,length(x));

for m=2:length(x)-1 Vx_c(m)=((x(m+1)-x(m-1)))/(2*deltat); Vy_c(m)=((y(m+1)-x(m-1)))/(2*deltat); end

%need correction for last index Vx_c(1)=Vx_c(2); Vy_c(1)=Vy_c(2);

Vx_c(end)=Vx_c(end-1); Vy_c(end)=Vy_c(end-1); deltat=x(2)-x(1);

plot(t,Vy_c)

Answer 1

[Heather Statt]

 here's the code:

theta0=40;
v0=25;
deltat=0.01;
[x,y,t]=projectile_simple(v0, theta0, deltat);

%%finite diference
%forward
Vx_f=zeros(1,length(x));
Vy_f=zeros(1,length(x));

for jj=1:length(x)-1
    Vx_f(jj)=(x(jj+1)-x(jj))/deltat;
    Vy_f(jj)=(y(jj+1)-y(jj))/deltat;
end

%need correction for last index
Vx_f(end)=Vx_f(end-1);
Vy_f(end)=Vy_f(end-1);
figure
hold on
plot(t,Vy_f)

%backward

Vx_b=zeros(1,length(x));
Vy_b=zeros(1,length(x));

for k=2:length(x)
    Vx_b(k)=(x(k-1)-x(k))/-deltat;
    Vy_b(k)=(y(k-1)-y(k))/-deltat;
end

%need correction for last index
Vx_b(1)=Vx_b(2);
Vy_b(1)=Vy_b(2);
%deltat=x(2)-x(1);

plot(t,Vy_b)
%
%central
Vx_c=zeros(1,length(x));
Vy_c=zeros(1,length(x));

for m=2:length(x)-1
    Vx_c(m)=((x(m+1)-x(m-1)))/(2*deltat);
    Vy_c(m)=((y(m+1)-x(m-1)))/(2*deltat);
end

%need correction for last index
Vx_c(1)=Vx_c(2);
Vy_c(1)=Vy_c(2);

Vx_c(end)=Vx_c(end-1);
Vy_c(end)=Vy_c(end-1);
deltat=x(2)-x(1);

plot(t,Vy_c)