Ballistic Trajectories

<BODY LANG="EN"> <HR><center> <table border=1> <td><img height=36 width=36 alt="" src="http://www.cs.utah.edu/icons/latex2html/previous_fade.gif"></td> <td><A NAME="tex2html9" HREF="../../../classes/Engineering/contents.html"><img height=36 width=36 alt="UP" src="http://www.cs.utah.edu/icons/latex2html/up.gif"></A></td> <td><A NAME="tex2html11" HREF="node1.html"><img height=36 width=36 alt="NEXT" src="http://www.cs.utah.edu/icons/latex2html/next.gif"></A></td> <td><a href="contents-uces-5.html"><img height=36 width=36 alt="CONTENTS" src="http://www.cs.utah.edu/icons/latex2html/toc.gif"></a></td> <td><a href="reset.hamlet"><img height=36 width=36 alt="RESET" src="http://www.cs.utah.edu/icons/latex2html/stop.gif"></a></td> <td><a href="copyright.html"><img height=36 width=36 alt="COPYRIGHT" src="http://www.cs.utah.edu/icons/latex2html/copyright.gif"></a></td> <td><a href="mailto:hamlet@cs.utah.edu"><img height=36 width=36 alt="FEEDBACK" src="http://www.cs.utah.edu/icons/latex2html/feedback.gif"></a></td> <td><a href="http://www.cs.utah.edu/%7Ehamlet/icons.html"><img height=36 width=36 alt="ABOUT" src="http://www.cs.utah.edu/icons/latex2html/about.gif"></a></td> </table> </center> <HR> <P> <H1>Ballistic Trajectories</H1> <P> <A NAME="visualization"> </A> In this lesson we will experiment with computing and visualizing <EM>ballistic trajectories</EM>. A ballistic trajectory is the path followed by an object which, after it is given some initial velocity, travels only under the influence of gravity. For the purposes of this lesson we will ignore the effects of air resistance. <P> The computational concept that we will focus upon in this lesson is visualization. In the five-step approach to solving computational problems, visualization is usually a form of <EM>assessment</EM>. Visualization is an extremely important engineering activity for a number of reasons: <P> <UL> <LI> The ability to visualize problems and their solutions makes it easier to develop and apply intuition. <LI> Mistakes in a solution often become readily apparent when the results are visualized. <LI> Visual aids are almost always necessary in order to effectively communicate engineering results. <P> </UL> <P> Collectively, the different types of visualization represent a significant fraction of <EM>all</EM> engineering activity. As a result, engineering has a rich tradition surrounding the use of simple plots. Plots represent represent the bulk of the visual aids used in engineering reports. Your ability to effectively incorporate plots into your writing will dramatically affect how your writing is perceived. Although effective communication is no substitute for quality work, it is probably the next most important factor in engineering success. <P> There are a wide variety of software packages available on workstations and personal computers for producing plots. Maple has a simple, though not especially flexible, plotting capability. In this lesson we will see how to use Maple to produce two-dimensional graphs, two-dimensional animations, and three-dimensional graphs. <P> As you advance in your career, you will doubtless use other plotting packages. You should keep in mind from the outset that even the fanciest package will be useless unless you know how to use plots to effectively convey information. <P> <HR><center> <table border=1> <td><img height=36 width=36 alt="" src="http://www.cs.utah.edu/icons/latex2html/previous_fade.gif"></td> <td><A NAME="tex2html9" HREF="../../../classes/Engineering/contents.html"><img height=36 width=36 alt="UP" src="http://www.cs.utah.edu/icons/latex2html/up.gif"></A></td> <td><A NAME="tex2html11" HREF="node1.html"><img height=36 width=36 alt="NEXT" src="http://www.cs.utah.edu/icons/latex2html/next.gif"></A></td> <td><a href="contents-uces-5.html"><img height=36 width=36 alt="CONTENTS" src="http://www.cs.utah.edu/icons/latex2html/toc.gif"></a></td> <td><a href="reset.hamlet"><img height=36 width=36 alt="RESET" src="http://www.cs.utah.edu/icons/latex2html/stop.gif"></a></td> <td><a href="copyright.html"><img height=36 width=36 alt="COPYRIGHT" src="http://www.cs.utah.edu/icons/latex2html/copyright.gif"></a></td> <td><a href="mailto:hamlet@cs.utah.edu"><img height=36 width=36 alt="FEEDBACK" src="http://www.cs.utah.edu/icons/latex2html/feedback.gif"></a></td> <td><a href="http://www.cs.utah.edu/%7Ehamlet/icons.html"><img height=36 width=36 alt="ABOUT" src="http://www.cs.utah.edu/icons/latex2html/about.gif"></a></td> </table> </center> <HR><P><ADDRESS> <I><A NAME="tex2html1" HREF="http://www.cs.utah.edu/~zachary">Joseph L. Zachary</A> <BR> <A NAME="tex2html2" HREF="http://www.cs.utah.edu/~hamlet">Hamlet Project</A> <BR> <A NAME="tex2html3" HREF="http://www.cs.utah.edu/">Department of Computer Science</A> <BR> <A NAME="tex2html4" HREF="http://www.utah.edu/ HTML_Docs/UofUHome.html">University of Utah</A></I> </ADDRESS> </BODY>