Projectile motion


This graphic shows projectile motion for both the first-order air resistance ("drag") and for the usually-assumed vacuum cases. The drag coefficient is k; when this is zero the drag trajectory is not shown. The Galileo complementary trajectory is shown only when the initial height y0 is zero. The units are SI. The velocity vectors are shown, and can be scaled by the vscale parameter (this changes the vector lengths to a convenient size).

The tscale parameter sweeps the time through a range of 0 to the current vacuum time of flight (TOF). The angle slider would not accept a negative value if the angles were in degrees so the slider reads out in radians. Use some common sense in interpreting the graphs, since it was not clear how, or was more trouble than it was worth, to limit things like using a negative angle if the initial height is zero.

The button at the lower left will sweep the time parameter so that the particle's motion and the velocity vector changes can be seen.

The ellipse option shows the positions of the trajectory maximum heights for a zero initial height and constant initial velocity. When this is enabled the Galileo trajectory is turned off, to reduce clutter.

Use the input bar at the bottom to define the parameters at exact values. The parameter y0 for example is entered as y_0 and Greek letters are available on this bottom toolbar. The toolbar button at the top, with the crossed arrows, permits zooming in/out and moving the entire plot range. After using this, press the arrow button at the left to return control of the sliders to the mouse. To get finer control over the movements, click a parameter name in the "Free Objects" list at the left of the figure, then use the arrow or + / - keys to change the parameter. Add "Control" to the arrow keys for faster changes.

A directory with PDF files is available; these documents contain background (derivations, etc.) for the equations used in this simulation, along with a lot of other interesting projectile-motion material. See /nikenuke/projectilePDF directory.

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WCEvans (9/09), Created with GeoGebra