some piece of shit

% starting values
Xo = 0
Yo = 0
Vo = 100
Oo = 2

% time (integrate) span
To = 0
Tf = 1

% constants
g = 10

% functions definition (divided by semicolon)
f = @(t,a) [a(3)*sin(a(4)); a(3)*cos(a(4)); -g*sin(a(4)); -g*cos(a(4))/a(3)];
% increasing accurasy
options = odeset('RelTol',1e-1,'AbsTol',[1e-4 1e-4 1e-4]);
% solving system by Runge–Kutta some class
[t, ft] = ode45(f, [To, Tf], [Xo Yo Vo Oo], options);

% plotting
figure
plot(t, ft(:,1), '-', t, ft(:,2), '-.', t, ft(:,3), '.', t, ft(:,4), '--')
plot(ft(:,1), ft(:,2))