Use MATLAB to program. The position of a projectile, fired with an initial speed

Question

Use MATLAB to program. The position of a projectile, fired with an initial speed of vo at an angle ?, can be written as a function of time (x(t),y(t)) as
x(t)=vocos(?)tandy(t)=vosin(?)t–0.5gt2
where g=9.81m/s2. The polar coordinates of the projectile (r(t),?(t)) at time t are:
r(t)=x2(t)+y2(t)???????????andtan(?(t))=y(t)x(t)
Write a MATLAB script to calculate the r(t) and ?(t) for input values of vo , ? , and t, provided by the user. Run the program for vo = 150 m/s and ? = 65° at time t = 5, 10, and 20 sec and report the results. Make sure to define your variables clearly and include proper comments in your code.

Explanation / Answer

%initialising given values for v0, alpha, g and times
v0 = 150;
alpha = 65;
g = 9.81;
times = [5, 10, 20];

%iterating through the times to calculate corresponding values at each time
for t=times
    %calculating x
    x = v0*cosd(alpha)*t;
    %calculating y
    y = v0*sind(alpha)*t - 0.5*g*t^2;
    %calculating r
    r = sqrt(x^2 + y^2);
    %calculating theta
    theta_t = atand(y/x);
  
    %displaying the values for r and theta at each time t
    disp(['At time t = ', num2str(t), ', r = ', num2str(r), ', theta = ', num2str(theta_t)]);
  
end

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