Projectile Motion Equation with inputs of degree and first velocity

I want to write a Matlab code about projectile motion equation for my project but after a while I am stuck.

I cant plot the V_x,t diagram and I want to change V_z equation after V_z = 0, when z has its max value, but I couldnt do this. Can you help me?

And its also debugging.

clc
clear all

v0 = 262.22 ; %m/s

g= 9.801 ; %m/s^2

theta_0 = 85 ; %derece

v0_x = v0*cosd(theta_0) ; %m/s

v0_z = -v0*sind(theta_0) ; %m/s

t = 0:0.01:80 ;

for i = 0: length(t)
    v_x = v0_x ;
    x = v0_x.*t ;
    
    v_z = g.*t + v0_z ;
    v_z(1) = v0_z ;
    z = 0.5*g.*t.^2 + v0_z.*t ;
    
    theta = atand( -v_z / v_x ) ;
    theta(1) = theta_0 ;
    
    if v_z == 0
  
        v_z = g.*t;
        
    end 
  
     figure(1)
     plot (t, theta) ;
    
     figure(2)
     plot (t, x) ;
       
     figure(3) 
     plot (t, -z) ;
 
     figure(4)
     plot (t, -v_z) ;

     figure(5)
     plot(t,v0_x) ;

     figure(6)
     plot(x,-z) ;
    
end 

[Davide Masiello]

Could you try write the problem equations?

[damla y]

yeah

I have 2 inputs which are V0 and Theta0

V0z= V0 sin theta0

V0x= V0 cos theta0

Vz= g t+ V0z

z= 0.5 g t^2+V0z

Vx=V0x

x= V0x t

theta= inverse tan(Vz/Vx)

[AndresVar]

@damla y I am curious why you want to change the v_z funciton at the peak, something happens to make it change?

Answer 1

[AndresVar]

Here is an example

Note you don't have to loop for each time value because matlab can perform calculations on the vector

Note: i changed v0_z and t and z a little, but you can see how it works in general.

v0 = 262.22 ; %m/s
g = 9.801 ; %m/s^2
theta_0 = 85 ; %derece
x0 = 0;
z0 = 0;

v0_x = v0*cosd(theta_0) ; %m/s
v0_z = v0*sind(theta_0) ; %m/s

t = 0:0.1:60;

% velocity
v_x = v0_x*ones(size(t));
v_z = -g*t+v0_z;

% position
x = v0_x.*t+x0;
z = -0.5*g*t.^2+v0_z*t+z0;

figure;
tiledlayout(3,1)
nexttile;
plot(x,z)
xlabel('x'),ylabel('z');
nexttile;
plot(t,v_x);
xlabel('t'),ylabel('v_x');
nexttile;
plot(t,v_z);
xlabel('t'),ylabel('v_z');

% to change v_z at maximum height
% for example here i set it to constant 2 m/s
% then the location also changes z=2*t+z0...
[~,peakIdx]=min(abs(v_z));
t2 = t(peakIdx:end)-t(peakIdx);
v_z(peakIdx:end)=2;
z(peakIdx:end)=2*t2+z(peakIdx);
figure
tiledlayout(1,2)
nexttile;
plot(t,v_z)
xlabel('t');ylabel('v_z');
nexttile;
plot(x,z);
xlabel('x');ylabel('z');