% script to bracket a solution to the constForce.m problem
% LAB1, PHYS220 Spring 2009

% givens (from problem statement)
x_o = 0; 
v_o = 30; 
a = -9.81;

% target values
v_target = 0; % particle at rest
x_target = 0; % particle returns to start

%% we'll do case for v = 0 first

% some constants & starting values
tol = 0.05;     % we'll allow a miss of up to this amount
t = 2;          % start at this time to find v = 0
step_t = 0.5;   % coarse starting search
div_t = 2;     % cut step in half on each bracket

% initial v
vars = constForce(t,[x_o v_o],a);

% for display purposes
disp(' ')
disp('    t (s)    v (m/s)    Dt (s)')
disp([t vars(2) step_t])

% search over angles, cut steps in half every time we pass target, display
% each step in the bracketing operation
while abs(v_target-vars(2)) > tol
    t = t + step_t;
    vars = constForce(t,[x_o v_o],a);
    disp([t vars(2) step_t])
    if sign(v_target-vars(2)) == sign(step_t)
        step_t = -step_t/div_t;
    end
end

%% now we'll look for x = 0 (the second instance)
% note the amount of code recycling here!

% some constants & starting values
tol = 0.05;     % we'll allow a miss of up to this amount
t = 5;          % start at this time to find v = 0
step_t = 0.5;   % coarse starting search
div_t = 2;     % cut step in half on each bracket

% initial v
vars = constForce(t,[x_o v_o],a);

% for display purposes
disp(' ')
disp('    t (s)    x (m)      Dt (s)')
disp([t vars(1) step_t])

% search over angles, cut steps in half every time we pass target, display
% each step in the bracketing operation
while abs(v_target-vars(1)) > tol
    t = t + step_t;
    vars = constForce(t,[x_o v_o],a);
    disp([t vars(1) step_t])
    if sign(v_target-vars(1)) == sign(step_t)
        step_t = -step_t/div_t;
    end
end


return