function [x, y, z, t] = freefall( p, v, h, dt )

% Calculates the path of a particle in freefall with given initial position
% and velocity, height to fall (fixed depth from origin), and time interval
% (in seconds).
% Returns an array of position and time (x, y, z, t) vectors. Assumes gravity
% is the only external force.  Calls freefall_step at each point.
% If h < 0, then |x| = |y| = |z| = 0 and |t| = 1.  This could be a problem.


i = 1;			% Index variable.

while (p(3) >= -h)	% Loop as long as the z variable has not fallen past h.
    x(i,1) = p(1);	% Store current x-value.
    y(i,1) = p(2);	% y-value.
    z(i,1) = p(3);	% z-value.

    [p, v] = freefall_step( p, v, dt );

    i = i + 1;		% Increment our index variable.
end

% Now we must make a time vector to match up with the others.

N = max(size(x));	% Length of x (and therefore t as well).

t(1,1) = 0;		% Initial time

for i = 2:N
    t(i,1) = t(i-1,1) + dt;
end

% Return [x, y, z, t]