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Projectile motion: targeting

This graphic shows a target (red dot) that can be moved around either by dragging it or using its x and y sliders. The premise is that an artillery piece with a fixed muzzle velocity is to be aimed to hit the target. Leaving the initial height and velocity constant, adjust the initial angle to try to hit the target. The solutions (there are usually two) can be shown, as can the "parabola of safety." Outside that parabola it is impossible to hit the target, with a given initial height and velocity. To move the trajectory with finer resolution, use the slider to get in the vicinity of the solution, then click on the angle parameter theta_0 in the "Free Objects" area on the left side. Then use the arrow or + and - keys to move the angle much more slowly. See the "Projectile Motion Math" activity for PDFs with details of the math behind this applet.