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plotProjectile MatLab Function - Pastebin.com
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- function [y_values] = plotProjectile(vi, p_angle, t_values)
- syms t
- g = 9.81;
- % y = vi * sin(alpha)t - 0.5*g(t^2)
- y(t) = vi * sind(p_angle) * t - 0.5 * g * (t^2);
- y_values = double(subs(y, t, t_values));
- plot(t_values, y_values, "Color", [1,0,0], "Marker","square");
- ylim([0 max(y_values)]);
- xlim([0 max(t_values)]);
- title("Projectile Motion with Tangent Vectors");
- xlabel("Time (seconds)");
- ylabel("Height (meters)");
- hold on
- % Getting derivative of y with respect to time to draw tanjent lines
- dy_dt = diff(y, t);
- dy_dt_values = double(subs(dy_dt, t, t_values));
- line_length = (t_values(2) - t_values(1));
- % Offset variable to make the text a little bit away from the
- % main graph to avoid overlapping
- vertical_offset = 0.2;
- for i = 1:length(t_values)
- %{
- Both the vectors y, t have the same size, so we can get y(t)
- values at each drawn point by using index of that element in
- vector, which I called ( i ) in my example.
- %}
- t0 = t_values(i);
- y0 = y_values(i);
- slope = dy_dt_values(i);
- %{
- line length should be equal square root of (dx)^2 + (dy)^2
- and dy = slope * dx where slope = dy/dx
- therefore line length = dx * square root of (1 + slope^2)
- and multiplied by 5 for scaling on the plot
- %}
- dx = (line_length * 5 / sqrt(1 + slope^2));
- quiver(t0, y0 , dx, slope * dx, 'b', 'LineWidth', 1, 'MaxHeadSize', 0.5);
- text(t0, y0 + vertical_offset, sprintf('v = %.2f', slope), ...
- 'FontSize', 8, 'Color', 'blue');
- % Drawing vertical and horizontal at each point
- quiver(t0, y0, 0, dx * slope, 'k', 'LineWidth', 1, 'MaxHeadSize', 0.5);
- quiver(t0, y0, dx, 0, 'k', 'LineWidth', 1, 'MaxHeadSize', 0.5);
- end
- legend("Projectile Path", "Tangent Vectors (V)", "Vertical and Horizontal Components");
- hold off
- end
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