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\documentclass{simiode}

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% With this version of the tex file and the associated SIMIODE.cls file you can produce BOTH a Student Version and a Teacher Version of your modeling scenario or technique narrative.
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% Basically the Student Version contains the title STUDENT VERSION along with the NAME OF SCENARIO, with no abstract, no keywords, no tags, no author identifiers, and no COMMENTS section. The Student Version contains only the STATEMENT of the modeling scenario with appropriate figures, data, instructions, and perhaps a bibliography appropriate for student resourcing, but nothing in the bibliography which would "give away" the nature of the modeling scenario, etc.
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%The Teacher Version contains the material in the Student Version, namely the title NAME OF SCENARIO, now headed with   TEACHER VERSION, but also full author  identification, abstract, key words, tag words, and, following the STATEMENT, a section of COMMENTS which can be discussion of presentation  ideas, "solutions," techniques, etc.
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% Authors can prepare a full Teacher Version using the notions immediately below  to create a pdf for review (but in review please eliminate all information about the author as we use a double-blind referee system. Such information will be restored when accepted and published in SIMIODE at www.simiode.org.
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\begin{document}

\newpage
% You only need to change the NAME OF SCENARIO in the next line and delete the footnote. See above for instructions on toggling from Teacher Version to Student Version.
\title{\ifnum\TeacherEdition=1 TEACHER VERSION \else STUDENT VERSION \fi\\UP DOWN}





\markboth{Up Down}{Up Down}






\author{Brian Winkel,
Director SIMIODE\\ 
Chardon OH 44024 USA USA\\
BrianWinkel@simiode.org
}

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\begin{abstract}
We model the height of a launched object which is subject to resistance proportional to velocity during  its flight. We ask questions about the motion as well, e.g., highest point or apex and terminal velocity.
\end{abstract}

\section*{SCENARIO DESCRIPTION}
 
An object of mass m is launched vertically upward from ground level with an initial velocity of $v_0$ and is slowed down by air resistance in the form of a force proportional to its velocity, i.e.  $k*v$.

\begin{itemize}
\item[(a)] Draw a free body diagram of the forces acting on the object.
\item[(b)] Use Newton's Second Law of Motion to build a differential equation of motion for its distance from the ground, s(t) in meters at time t in seconds.
\end{itemize}

Now suppose we know the mass of the object is 2.1 kg,  $g = 9.8$ m/s$^2$, $k = 3$ N/(m/s); and the initial height is $s(0) = 0$ m.

\begin{itemize}
\item[(c)] Solve the differential equation in (b) for $s(t)$.
\item[(d)] Determine the time and height at which the object comes to rest at the apex of its journey.
\item[(e)] Determine the time at which the object returns to the ground.
\item[(f)] Determine the distance traversed by the object in $t$ seconds.
\item[(g)] Find the time(s) when the upward speed is the same as the downward speed in magnitude and is 6 m/s.
\item[(h)] Find the terminal velocity of the downward falling object if it were allowed to fall indefinitely without striking the ground and determine just how close to this terminal velocity the object comes. 
\end{itemize}

\teacher{
\section*{NOTES FOR TEACHERS}

We give complete steps for the analysis in a Mathematica notebook, 3-065-T-Mma-UpDown-TeacherVersion.nb and a pdf file for those who do not have access to Mathematica. This is rather a routine problem in which we use a Free Body Diagram to derive the equation of motion for the object according to Newton's Second Law of Motion and then use it to address the remaining issues.

}
\end{document}




