The Ballistic Trajectory Problem

<BODY LANG="EN"> <HR><center> <table border=1> <tr valign=top> <td><A HREF="uces-5.html"><img height=36 width=36 alt="PREVIOUS" src="/UCESIcons/tools/previous.gif"></A></td> <td><A HREF="uces-5.html"><img height=36 width=36 alt="UP" src="/UCESIcons/tools/up.gif"></A></td> <td><A HREF="node2.html"><img height=36 width=36 alt="NEXT" src="/UCESIcons/tools/next.gif"></A></td> <td><a href="contents-node1.html"><img height=36 width=36 alt="CONTENTS" src="/UCESIcons/tools/toc.gif"></a></td> <td><a href="/hamlet-bin/qhandler?exit" target="results"><img height=36 width=36 alt="RESET" src="/UCESIcons/tools/stop.gif"></a></td> <td><a href="http://www.cs.utah.edu/~hamlet/"><img height=36 width=36 alt="HAMLET" src="/UCESIcons/tools/hamlet.gif"></a></td> <td><a href="copyright.html"><img height=36 width=36 alt="COPYRIGHT" src="/UCESIcons/tools/copyright.gif"></a></td> <td><a href="mailto:uces_info@krellinst.org"><img height=36 width=36 alt="FEEDBACK" src="/UCESIcons/tools/feedback.gif"></a></td> <td><a href="http://www.cs.utah.edu/~hamlet/icons.html"><img height=36 width=36 alt="ABOUT" src="/UCESIcons/tools/about.gif"></a></td> </tr> </table> </center> <HR> <H1>The Ballistic Trajectory Problem</H1> <P> One of the first problems studied in an introductory physics class is the ballistic trajectory problem. Let's assume that we are standing in a flat field and that we throw a ball so that it starts out moving at some velocity <nobr><I>V</I> > 0</nobr> and at some angle <IMG WIDTH=78 HEIGHT=27 ALIGN=MIDDLE ALT="0 .LE. theta .LE. pi/2" SRC="img1.gif"> radians with the ground. At any given time <I>t</I>, the ball's horizontal distance is given by <P> <IMG WIDTH=281 HEIGHT=15 ALIGN=BOTTOM ALT="Vt cos(theta)" SRC="img2.gif"> <P> and its vertical height is given by <P> <IMG WIDTH=307 HEIGHT=34 ALIGN=BOTTOM ALT="Vt sin(theta) - (1/2)gt^2" SRC="img3.gif"> <P> where <I>g</I> is the earth's gravitational constant, or 9.8 meters/sec/sec. This assumes that the ball's initial horizontal and vertical positions are both 0. It will prove convenient to define functions <TT>distance</TT> and <TT>height</TT> that take initial velocity, initial angle, and time as arguments and return the distance and height of the ball. See if you can do that yourself before looking at our solutions. <P> <A NAME="tex2html5" HREF="answer33.html">Click here for the answer</A><P> <HR><center> <table border=1> <tr valign=top> <td><A HREF="uces-5.html"><img height=36 width=36 alt="PREVIOUS" src="/UCESIcons/tools/previous.gif"></A></td> <td><A HREF="uces-5.html"><img height=36 width=36 alt="UP" src="/UCESIcons/tools/up.gif"></A></td> <td><A HREF="node2.html"><img height=36 width=36 alt="NEXT" src="/UCESIcons/tools/next.gif"></A></td> <td><a href="contents-node1.html"><img height=36 width=36 alt="CONTENTS" src="/UCESIcons/tools/toc.gif"></a></td> <td><a href="/hamlet-bin/qhandler?exit" target="results"><img height=36 width=36 alt="RESET" src="/UCESIcons/tools/stop.gif"></a></td> <td><a href="http://www.cs.utah.edu/~hamlet/"><img height=36 width=36 alt="HAMLET" src="/UCESIcons/tools/hamlet.gif"></a></td> <td><a href="copyright.html"><img height=36 width=36 alt="COPYRIGHT" src="/UCESIcons/tools/copyright.gif"></a></td> <td><a href="mailto:uces_info@krellinst.org"><img height=36 width=36 alt="FEEDBACK" src="/UCESIcons/tools/feedback.gif"></a></td> <td><a href="http://www.cs.utah.edu/~hamlet/icons.html"><img height=36 width=36 alt="ABOUT" src="/UCESIcons/tools/about.gif"></a></td> </tr> </table> </center> <HR> <P><ADDRESS> <I> <A HREF="http://www.cs.utah.edu/~zachary">Joseph L. Zachary</A> <BR> <A HREF="http://www.cs.utah.edu/~hamlet">Hamlet Project</A> <BR> <A HREF="http://www.cs.utah.edu/">Department of Computer Science</A> <BR> <A HREF="http://www.utah.edu/">University of Utah</A> </I> </ADDRESS> </BODY>