a)
function [vx , vy] = initVelocity(initialAngle, speed) vx = cosd(initialAngle)*speed; vy = sind(initialAngle)*speed; end
b)
function [x, y] = position(x,y, vx, vy, dt) x = x + vx*dt; y = y + vy*dt; end
c)
function [ ax , ay ] = acceleration (vx ,vy) k = 0.01; g = 9.81; ax = -k*vx*abs(vx); ay = -k*vy*abs(vy)-g; end
d)
function [vx , vy] = velocity(ax, ay, vx, vy, dt) vx = vx + ax * dt; vy = vy + ay * dt; end
e)
function [x, y] = trajectory(initialSpeed, initialAngle, height) dt =0.01; xPos = 0; % Nåværende verdi for x yPos = height ; % Nåværende verdi for y [vx , vy] = initVelocity(initialAngle ,initialSpeed); i = 1; while yPos > 0 % kalkuler akselerasjon [ax , ay] = acceleration(vx, vy); % kalkuler fart [vx , vy] = velocity(ax, ay, vx, vy, dt); % kalkuler endring i distanse [xPos, yPos] = position (xPos, yPos, vx, vy, dt); x(i) = xPos; y(i) = yPos; i = i + 1; end end
f)
function plotTrajectory(initialSpeed, initialAngle, height) [x, y] = trajectory(initialSpeed, initialAngle, height); plot (x, y); grid on; xlabel('x'); ylabel('y'); title('plotTrajectory'); end
g)
function plotTrajectoryLength (initialSpeed, start, step, stop, height) initialAngles = start:step:stop; n = length(initialAngles); lengths = zeros(n,1); for i = 1:n [x, y] = trajectory(initialSpeed, initialAngles(i), height); j = length (x); lengths (i) = x(j); end plot (initialAngles ,lengths); xlabel('Angle'); ylabel('y'); grid on; title('plotTrajectoryLength'); end
Det kan virke som om pi/4 (45 grader) gir lengst støt. Dette virker intuitivt korrekt.
Jo høyere man kaster fra, jo bedre er det å kaste mest mulig rett frem (i x-retning).