Projectile motion with loop function

I need to create a loop for the projectile motion of a ball

I plot it but it continue even once the y-position is below 0 (the floor)

    clc
  clear all

V0=100 %%%Initial velociton
Sx0=0 %%%Initial x-position
Sy0=0 %%%Initial y-position
angle=45 %%%angle of projection
g=9.807 %%%Gravitational constant 
ymin=0 %%%minimum value for y-position

t = 0:0.1:20 %%%Time
Vx=V0*cos(angle); %%%x-velocity
Vy=V0*sin(angle); %%%y-velocity

Sx=Sx0+Vx*t %%%x-position 
Sy=Sy0+(Vy*t)-(0.5*g*t.^2) %%%y-position 

if Sy>=min
    plot (Sx,Sy)
end

grid on

Answer 1

[BhaTTa]

To simulate the projectile motion of a ball and stop the simulation once the y-position goes below the floor (y = 0), you can use a loop that updates the position and velocity of the ball at each time step. Here's how you can modify your code to include this logic:

clc;
clear all;

% Parameters
V0 = 100; % Initial velocity (m/s)
Sx0 = 0; % Initial x-position (m)
Sy0 = 0; % Initial y-position (m)
angle = 45; % Angle of projection (degrees)
g = 9.807; % Gravitational constant (m/s^2)
ymin = 0; % Minimum value for y-position (the floor)
dt = 0.1; % Time step (s)

% Convert angle to radians
angle_rad = deg2rad(angle);

% Initial velocities
Vx = V0 * cos(angle_rad); % x-velocity (m/s)
Vy = V0 * sin(angle_rad); % y-velocity (m/s)

% Initialize positions
Sx = Sx0;
Sy = Sy0;

% Initialize time
t = 0;

% Initialize arrays to store positions for plotting
Sx_array = [];
Sy_array = [];

% Loop to update positions and velocities
while Sy >= ymin
    % Update positions
    Sx = Sx + Vx * dt;
    Sy = Sy + Vy * dt - 0.5 * g * dt^2;
    
    % Update y-velocity
    Vy = Vy - g * dt;
    
    % Update time
    t = t + dt;
    
    % Store positions for plotting
    Sx_array = [Sx_array, Sx];
    Sy_array = [Sy_array, Sy];
end

% Plot the trajectory
plot(Sx_array, Sy_array);
xlabel('x-position (m)');
ylabel('y-position (m)');
title('Projectile Motion of a Ball');
grid on;

Explanation

1. Parameters: Define the initial conditions, gravitational constant, and time step.
2. Convert Angle to Radians: Convert the projection angle from degrees to radians.
3. Initial Velocities: Calculate the initial velocities in the x and y directions.
4. Initialize Positions: Set the initial positions.
5. Initialize Time: Set the initial time to zero.
6. Initialize Arrays: Create arrays to store the positions for plotting.
7. Loop: Use a while loop to update the positions and velocities at each time step until the y-position (Sy) goes below the minimum value (ymin).

• Update the x and y positions using the current velocities and time step.
• Update the y-velocity to account for the effect of gravity.
• Increment the time by the time step.
• Store the current positions in the arrays.

1. Plot the Trajectory: Plot the stored x and y positions to visualize the projectile motion.

This code will simulate the projectile motion of the ball and stop the simulation once the ball hits the floor (y = 0). Adjust the parameters as needed for your specific scenario.