Homework Assignment

<BODY LANG="EN"> <HR><center> <table border=1> <tr valign=top> <td><A HREF="node8.html"><img height=36 width=36 alt="PREVIOUS" src="/UCESIcons/tools/previous.gif"></A></td> <td><A HREF="uces-6.html"><img height=36 width=36 alt="UP" src="/UCESIcons/tools/up.gif"></A></td> <td><A HREF="node10.html"><img height=36 width=36 alt="NEXT" src="/UCESIcons/tools/next.gif"></A></td> <td><a href="contents-node9.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@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>Homework Assignment</H1> <P> The following problems all involve the destroyer power problem. <P> <OL> <LI> Suppose that you have available only the <TT>power1</TT> function, and you want to study the power requirements of a particular destroyer on a particular trajectory. You'd like to obtain a <TT>power</TT> function that takes only time as a parameter. How can you use <TT>unapply</TT> to do so? In what ways is the function that you derive more efficient to use than the original four-argument function? (We're concerned with computational efficiency here--not typing efficiency!) <P> <LI> Define a <TT>power2</TT> function that is just like <TT>power1</TT> except that it takes <EM>velocity</EM> as an argument in place of <EM>position</EM>.<LI> Suppose that we'd like to move our destroyer on a straight line back and forth between points 1000 meters from either side of the origin. Suppose that the following equation gives our position (in meters) as a function of time: <P>  <DD><I>p</I>(<I>t</I>) = 1000 cos(<I>t</I>/<I>a</I>) <P> where <I>a</I> is some constant. Small values for <I>a</I> will describe a faster oscillation, and large values will describe a slower oscillation. By doing graphical experiments using different values for <I>a</I>, what is the smallest amount of time in which the destroyer can move from the origin, out to +1000 meters, back to -1000 meters, and then back to the origin without exceeding the 5 megawatt peak power capacity of the destroyer? <P> <LI> When you see a negative power on a power plot, it means that the destroyer is using its engines to slow itself down. Why are the positive peaks on the power plots you produced in answering the last question more extreme than the negative peaks? <P> </OL> <P> <HR><center> <table border=1> <tr valign=top> <td><A HREF="node8.html"><img height=36 width=36 alt="PREVIOUS" src="/UCESIcons/tools/previous.gif"></A></td> <td><A HREF="uces-6.html"><img height=36 width=36 alt="UP" src="/UCESIcons/tools/up.gif"></A></td> <td><A HREF="node10.html"><img height=36 width=36 alt="NEXT" src="/UCESIcons/tools/next.gif"></A></td> <td><a href="contents-node9.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@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>