Question

Create a program that plots the trajectory, from the initial height to the ground, of a projectile accelerating both in the horizontal and vertical directions.

-Matlab Code

PROBLEM 4: In your physics class, projectile motion has two components: constant-velocity motion in the horizontal direction and free-fall motion in the vertical direction. However, in reality, the horizontal motion has acceleration due to air resistance, wind, and other factors. The goal of this problem is to visualize the trajectory of a projectile for both ideal and non-ideal motion. Create a program that plots the trajectory, from the initial height to the ground, of a projectile accelerating both in the horizontal and vertical directions. The program must accept the following as inputs: • • • the initial height of the projectile above the ground in meters; the magnitude of the velocity in m/s; the angle in degrees with respect to the +x-axis at which the projectile is fired; the x-component of the acceleration, considering the sign, in m/s2; the y-component of the acceleration, considering the sign, in m/s2; The program must also have error detection for the instance the user inputs zero acceleration for the vertical component. (If the vertical acceleration is zero, then there would be no free fall.) You may use the error command.

Answer 1

Problem 4:

MATLAB CODE:

% User input

h0 = input('Enter initial height (in meters): ');

u = input('Enter initial velocity (in m/s): ');

theta = input('Enter angle (in degrees): ');

theta = theta*pi/180;

ax = input('Enter x-component of acceleration (in m/s^2): ');

ay = input('Enter y-component of acceleration (in m/s^2): ');

x = [0];

y = [h0];

t = 0;

disp_x = u*cos(theta)*t + ax*t^2/2;

disp_y = h0 + u*sin(theta)*t + ay*t^2/2;

% Keep looping till displacement in y direction is > 0

while disp_y >= 0

    x = [x disp_x];

    y = [y disp_y];

    t = t + 0.1;

    disp_x = u*cos(theta)*t + ax*t^2/2;

    disp_y = h0 + u*sin(theta)*t + ay*t^2/2;

end

x = [x disp_x];

y = [y disp_y];

% Plot the trajectory

plot(x, y);

title('Trajectory');

xlabel('x');

ylabel('y');

ylim([0 inf]);

SAMPLE OUTPUT:

Enter initial height (in meters): Enter initial velocity (in m/s): 45 Enter angle (in degrees): 30 Enter x-component of acceleration (in m/s^2): 2 Enter y-component of acceleration (in m/s^2): -9.8 >> COMMAND WINDOW

Trajectory 30 25 20 > 15 10 50 100 150 200 250

FOR ANY HELP JUST DROP A COMMENT