I am finally learning something in basic physics which I have wanted to know for some time, namely how to track the movement of a projectile launched above the earth's surface at an angle. I have worked through, more than once, trajectories of things projected directly upwards, and things moving horizontally. But the angles in between are where arrows, cannonballs, artillery shells, and home run balls hit by Red Sox sluggers Manny Ramirez and David Ortiz travel. The mathematics of their paths, at least in the abstract without taking air resistance into account, are dictated by trigonometry, and are much more exactly described by calculus. Of course in baseball, air resistance is an essential part of how the ball travels, especially in seaside Boston. This will be covered in a later chapter, when I get further into my reading of THE PHYSICS OF BASEBALL by physicist and baseball-lover Robert K. Adair. His author photograph shows him wearing a Boston Red Sox hat, so assuming him to be a Boston fan, I respect him greatly. I am not sure he is still alive, but I do hope he lived to see the Great Victory of 2004.

So I had to learn trigonometry before I could begin to fathom those parabolic trajectories of things thrown or propelled into the air. The graphs in Schaum's are as helpful as they can be, but I have added all sorts of notes in different colors, hoping that they will make sense to me the next time I go through this material. The problem for me is that these calculations, even if they disregard air resistance, cover at least two sets of variables: velocity and displacement. Each of these is a vector quantity and the graphs for them look alike. The graphs are so alike that at first I didn't know which one went with which. The graph for displacement looked deceptively like a picture of the object's trajectory over time. So did the graph for velocity vectors. Both of these graphs are indeed related to what the path of the object looks like when it's traveling, but they are not actually pictures of the object in motion.

Let us turn to volcanology, my first love in science. Volcanoes of a somewhat more peaceful sort emit what are called "Strombolian" bursts of fiery material, named after the famous Mediterranean volcano Stromboli.

This photograph shows a volcanic vent (not Stromboli, though) spewing forth such a burst. The time exposure needed to take the photo shows the complete trajectories of volcanic bombs, as they rise and fall. They trace perfect parabolas. These are not graphs, though they can easily be mathematically described. The photo, and other artistic representations of projectile paths, are pictures. Yet they, too, convey information about motion, more vividly than an x/y graph. As a visual artist I will always feel the tension between mathematical graphs and pictured illustrations.

Posted at 3:13 am | link