\documentclass[12pt]{report}
\usepackage{amsmath,amsfonts}
\usepackage{geometry,graphics}
\geometry{paperheight=11in,paperwidth=8.5in,tmargin=1.0in,bmargin=1.0in,inner=1.00in,outer=1.00in}
% \ilf is inline formula in displaystyle
\newcommand{\ilf}[1]{$\displaystyle #1 $}
\newcommand{\calc}[1]{\framebox[1.3\width]{\bf #1}}
\renewcommand{\today}{Fall 2024}

\begin{document}
\thispagestyle{empty}
\noindent{\bf Math 2326\hfill Worksheet \#1\hfill\today}\medskip\\
\noindent{\bfseries\itshape Bungee Jumping}\medskip\\
\begin{enumerate}
\item Sketch a possible bungee jump in the graph below. Here $t$ denotes time (in seconds), while $y(t)$ denotes the vertical position of the jumper at time $t$. The jump starts at the ``dot''. 

The $t$-axis is chosen so that the vertical distance between the initial position (the ``dot'') and the $t$-axis is the natural length of the bungee cord (without any mass attached).

\textbf{Do this last. Think about Steps 2--4 first.}
\begin{figure}[h]
\begin{center}
\resizebox{.85\textwidth}{!} {\includegraphics{WS011.pdf}}
\end{center}
\end{figure}
\item Where will the bungee jumper be located at the end of the jump, i.e., what can you say about $\displaystyle{\lim_{t\to\infty} y(t)}$?\vfill
\item When will the jump feel most unpleasant, i.e., when is $|y''(t)|$ maximal?\vfill 
\newpage
\item Sketch the graph of  $y''(t)$. (You may also want to sketch $y'(t)$.)
\begin{figure}[h]
\begin{center}
\resizebox{.85\textwidth}{!} {\includegraphics{WS012.pdf}}
\end{center}
\end{figure}
\end{enumerate}
\end{document}
