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{ \Large Physics 441\\
Exam 2\\
\vspace{0.5cm}
Eastern Oregon University\\
Fall 2000
Instructor: Anthony A. Tovar, Ph. D.}
\end{center}
\noindent
Write a report about projectile motion which includes the
effects of air
resistance. Your report will include the numerical simulation
of the required differential equations done in two ways:
C program and Maple.\\
\noindent
The format for your report should be as follows:
\begin{enumerate}
\item Abstract.
\item Introduction.
\item Theory.
\item Results.
\item Conclusion.
\item Appendices.
\item References.
\end{enumerate}
\noindent
The
\textbf{Abstract}
should be two or three sentences overviewing
the contents of the report.\\
\noindent
The
\textbf{Theory}
should include the derivation of the equations
used in your model of air resistance and be a discussion
of the model used. The model you should use has a linear
and quadratic velocity components for the force on your
assumed spherical object of the form
\begin{equation}
\mathbf{F} = -c\mathbf{v} - c_2 \mathbf{v} | \mathbf{v} |
\end{equation}
\noindent
The
\textbf{Results} should contain a solution and have a
discussion of the numerical solution. You should
also discuss other effects which you didn't but
could include (such as earth curvature, variable
gravity, variable air resistance, wind resistance,
etc.)\\
\noindent
Make plots of range optimizing angle (in degrees!) vs. initial projectile speed
for spherical baseball-densitied projectiles of radius
0, .1 mm, 1 mm, 1 cm, 10 cm, 1 m, 10 m.
Of course, the optimum angle for low-velocity objects is 45 degrees.
\noindent
The
\textbf{Conclusion}
should contain a paragraph or two summarizing
your results.\\
\noindent
Appendix A should contain your C program(s) and
Appendix B should contain your Maple script(s).
If there are other appendices, they should be included
here as well.\\
\noindent
You should use the numerical
\textbf{Reference}
system. Your
text has no references to the linear and quadratic
velocity models (naughty, naughty). See if you can
find some. You should also reference your text.\\
\noindent
The following is a list containing the types of things your
report should include (that your homework assignment didn't):
\begin{enumerate}
\item Fix Kluge in Maple Script.
\item Better Commenting in Maple Script.
\item vary dt in c program until plots no longer change.
\item Use Runge-Kutta to solve differential equations in
c program.
\end{enumerate}
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