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\begin{document}

{\large Names:}
\bigskip

\centerline{\bf \Large Moving in two dimensions}
\bigskip

Imagine a child Emily taking a short walk starting from her
front porch. For each of the following situations, calculate two
things:
\begin{itemize}
\item the total distance that Emily walked, 
\item how far Emily is from her front porch at the end of the
walk, and in what direction.
\end{itemize}

For each case,  draw a sketch of the path she took (take 1
grid= 1 foot).  Don't simply estimate the distances from the
plot, instead use trigonometry to find the exact values of
the distances asked for above.  



\begin{enumerate}
\item She walks $3$ feet east, then $4$ more feet east.

\psfig{figure=Patsy:Documents:pictures:nwse.eps,height=2.41in,width=3.48in}

\vfill




\item She walks $3$ feet east, then $4$ feet west.

\psfig{figure=Patsy:Documents:pictures:nwse.eps,height=2.41in,width=3.48in}

\vfill

\clearpage

\item She walks $3$ feet east, then $4$  feet north.

\psfig{figure=Patsy:Documents:pictures:nwse.eps,height=2.41in,width=3.48in}
\vfill

\item She walks $3$ feet west, then $4$ feet south.

\psfig{figure=Patsy:Documents:pictures:nwse.eps,height=2.41in,width=3.48in}
\vfill

\item She walks $3$ feet east, then $4$ feet northeast.

\psfig{figure=Patsy:Documents:pictures:nwse.eps,height=2.41in,width=3.48in}

\vfill
\clearpage

\item She walks $3$ feet $30$ degrees north of east, then
$4$ feet $80$ degrees north of east.

\psfig{figure=Patsy:Documents:pictures:nwse.eps,height=2.41in,width=3.48in}

\item Look back on  the work you have done to this point.  
\begin{enumerate}
\item What
procedure have you used to calculate the total distance
traveled?
\vfill
\item What procedure have you used to calculate the distance
she is from her front porch?
\vfill
\item If you haven't done so already, state a procedure that
will work {\it that does not rely on drawing a sketch}.  Then
use this method to calculate the distance from her front porch
in the next situation.  
\vfill
\end{enumerate}

\clearpage

\item She walks $3$ feet 30 degrees south of west, 
then $4$ feet northeast.

\psfig{figure=Patsy:Documents:pictures:nwse.eps,height=3.133in,width=4.524in}

\vfill


\item In your above procedure, how do you differentiate
distances traveled east from those traveled west?  North from
south?
\vfill


\item Can you easily calculate the distance from her front
porch using the sketch?
\vfill

\end{enumerate}

\end{document}