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\hskip36pc \= Math.\ 302-01\\
\>Spring, 2005\\
\>R. B. Kearfott
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\bf Second Examination \\
\it Friday, February 4, 2005
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\noindent {\small {\bf Instructions:} This exam should be done on
your own paper. Your name should be on each sheet and on the back of
the last sheet; the answers should appear written carefully and in
order. If in doubt, show intermediate steps: Full credit may not be
given, even for correct answers, unless work is arranged clearly and
explained. This exam is closed book. You may leave after handing in
your exam paper, but be sure to check your answers carefully. You
may keep this exam sheet.  Each entire problem is worth 30 points,
while 10 points are free.}

\Large
\begin{enumerate}
   \item Write down an equation for the plane through the points
         $(-1,-1,-1)$, $(1,-1,-1)$, and $(-1,-1,1)$.  Show all of your
         work.
   \item A wind blowing from the north is applying a force of 35
         pounds on a bicyclist traveling to the northeast (that is, at
         an angle of $45^{\circ}$) at 15
         miles per hour.  How much work, in foot-pounds, does the
         cyclist expend to counteract the wind over a period of 3
         hours?  Draw a diagram, and show all of your work.
         (\textit{Hint: Be sure to multiply miles by 5280 to get
         feet.})
   \item An airplane traveling 750 kilometers per hour encounters a
         wind blowing at 125 kilometers per hour from an angle
         10 degrees south of due west.  (That is, the wind is
         blowing from 10 degrees south of west to 10 degrees north
         of east.)
         \begin{enumerate}
            \item In what direction should the plane travel so that
                  its motion with respect to the ground is from due
                  west to due east?
            \item What is the plane's ground speed when it is
                  traveling in that direction?
         \end{enumerate}
         Draw a diagram, and show all of your work.
         (\textit{Hint: Make sure your calculator is set to degrees,
         if you are using degrees, and make sure your calculator is
         set to radians, if you are using radians.})
\end{enumerate}

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