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{\bf ADVANCED DYNAMICS --- PHY 4241/5227}\\\vspace {2mm} 
{\bf Final -- Problem 2}\\%
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\begin{description}

\item{(1)} There are many equivalent formulations. For instance,

\item{(1a)} Galilei invariance: The laws of nature are independent
of any uniform, translational motion of the reference frame.

\item{(1b)} The speed of light in empty space is independent of 
the motion of its source.  \bigskip

\item{(2a)} 
$$ \triangle t = \frac{\tau}{\sqrt{1-(0.99)^2}} = \frac{\tau}{0.141} =
   \triangle t = \frac{2.6\times 10^{-8}\,s}{0.141}\,\rm s = 
   1.84\times 10^{-7}\,s$$
\item{(2b)} 
$$ \triangle x = \triangle t\times 0.99\,c = 54.7\,m~~(c\ \rm speed\
   of\ light)\,.$$
\end{description}

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% \caption{Ladder for assignment~14.} \label{fig_lader} \end{figure}

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