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\begin{document}

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\begin{center}
\large
Math 120 - Summer 2006 \pp
Midterm 2 \pp
August 3, 2006 \pp
\end{center}
\normalsize
\vfill
\medskip
\hfill Name: \hrulefill \hrulefill \hrulefill
\hspace{0.5in}
%Section: \hrulefill
Section: C
\vfill
\begin{center}
{\large
\begin{tabular}{||c|r|r||} \hline 
    1     & 10 &\hspace{10mm} \hfill\\ \hline 
    2     & 8 & \\ \hline
    3     & 7 & \\ \hline
    4     & 10 & \\ \hline
    5     & 15 & \\ \hline
    Total & 50 & \\ \hline 
\end{tabular}
}
\end{center}
\vfill
\begin{itemize}
    \item You may use a calculator during this examination.  
          Other electronic devices are not allowed, and should be
          turned off for the duration of the exam.
    \item \textbf{When computing values of $\sin, \cos,$ and $\tan$ on your calculator,
          make sure you are using the correct angle mode (degrees or radians)!}
    \item If you use a trial-and-error or guess-and-check method, or read a
          numerical solution from a graph on your calculator when an algebraic
          method is available, you will not receive full credit.
    \item You may use one hand-written 8.5 by 11 inch page of notes.
    \item Show all work for full credit.  
    \item You have 60 minutes to complete the exam. 
    \item Good luck!
\end{itemize}

\newpage

\begin{enumerate}

\item \emph{(10 points)}
\begin{enumerate}
\item
Find the length $x$ in the figure below.

\includegraphics{Triangle.pdf}

\vfill
%\item If $\displaystyle \cos(\theta) = \frac{3}{\sqrt{9+z^2}}$, find $\sin(\theta)$.  (Hint: label the sides of the triangle below.)

%\includegraphics{Triangle2.pdf}
%\vfill


\item Find all values of $\alpha$ (in radians!) between $-\pi$ and $2\pi$ that satisfy $\sin(\alpha) = -\frac{2}{3}$.
\vfill
\end{enumerate}

\newpage

\item 
\begin{minipage}[t]{20cm}
\begin{minipage}[t]{9cm}
\emph{(8 points)} On the old penny farthing bicycles, the pedals turn at the same angular
speed as the large wheel.  Suppose on the bicycle shown, the large wheel is 55
inches in diameter, and the small wheel is 19 inches in diameter.
\\

Suppose you pedal at 2 revolutions per second. What's the angular velocity of
the small wheel?  How fast (in mi/hr) are you going?  \vfill
\end{minipage}
\hfill
\begin{minipage}[t]{10cm}
\mbox{} \\
%\includegraphics{pennyfarthing.jpg}
\scalebox{0.5}{\includegraphics{pennyfarthing.jpg}}
\end{minipage}
\end{minipage}

\vfill

\newpage
\item \emph{(7 points)}  
The height of a ball is given by $h(t) = -t^2 + 4t$, for $0 \le t \le 4$.  Restrict the domain
of $h(t)$ to where the height is increasing, and find the inverse function.
What is the domain of the inverse function?

\scalebox{1}{\includegraphics{ballpath-1.pdf}}
\vfill



\newpage

\item \emph{(10 points)}  
Milo is working on his golf swing.  The more he practices, the more accurate he gets.  If he doesn't practice at all he can get within 35 feet of the hole; if he practices for 3 hours, he can get within 25 feet of the hole.  No matter how much he practices, Milo cannot get closer than 10 feet.  Assume that his accuracy is modeled by a linear-to-linear function.

\begin{enumerate}
\item Find the function that gives his distance to the hole as a function of
hours he practices.
\vfill

\item How much does Milo need to practice if he wants to get 15 feet from the hole?
\vfill

\end{enumerate}

\newpage

\item
\begin{minipage}[t]{20cm}
\begin{minipage}[t]{12cm}
\emph{(15 points)} Remember Tiff, the carnival owner who tried to design the world's largest
ferris wheel?  Tiff has decided to create a new ride, called \emph{The
Springalizer}, where you bounce up and down in a box attached to a giant
spring.  She's had another vision, and wants the ride to work like this:  
\\
The
box should be at its highest point, 10 feet off the ground, at $t = 2$ seconds 
after the ride starts; it should return to the highest point 7 seconds later.
Finally, she wants the amplitude of the oscillation to be 6 feet.
\end{minipage}
\hfill
\begin{minipage}[t]{7cm}
\mbox{} \\
\includegraphics{Springalizer.pdf}
\end{minipage}
\end{minipage}


\begin{enumerate}
\item Give a sinusoidal function $h(t)$ for the height of the box after $t$ seconds.
\vfill
\item Tiff tries the ride out, and the box crashes into the ground.  When does this happen?
\vfill
\newpage
\item What is the largest possible amplitude so that the box just touches the ground?


\end{enumerate}
\end{enumerate}


\end{document}

