In an experiment similar to Lab 3, a plummet falls under the force of gravity
with its position recorded every 0.05 seconds on a spark tape. 
The location of the plummet 
(<em>y</em>, in m) from the release point 
is measured at each spark point.  The accuracy of these positions measurements
is .005&nbsp;m.
Newton predicts that the location
of the plummet will fit a quadratic relationship:

<p><em>y</em> = <em>y</em><sub>0</sub> + <em>v</em><sub>0</sub> <em>t</em> + 0.5 <em>g t</em><sup>2</sup>

<p>where <em>g</em> is the acceleration of gravity and
<em>y</em><sub>0</sub> and <em>v</em><sub>0</sub> are the plummet's initial position and velocity.

<p> So:
<p> <em>g</em> = <em>2C</em>

<ol>
<li>Fit this data with a quadratic relationship.
<li>Consider Newton's scientific claim of an quadratic law.
Does this evidence (data) confirm or contradict this claim?  Support
your answer quantitatively.
<li>Properly report (sigfigs, error, units) the <em>A</em>, <em>B</em> and <em>C</em>
parameters of the best-fit relationship.
<li>Use a spreadsheet to calculate <em>g</em> from <em>C</em>.
<li> Properly report 
(sigfigs, error, units) the value for <em>g</em>. 
<li>Self-document the spreadsheet and turn in a hardcopy of the page.
<li>Make a hardcopy plot of the data with best-fit curve. 
</ol>
<p><table style="text-align: center; width: 300px;" border=1 cellpadding=2 cellspacing=2>
 <tr><th>X<br>(s)<th>Y<br>(m)
 <tr><td>0.05<td>5.4E-2
 <tr><td>0.10<td>0.111
 <tr><td>0.15<td>0.213
 <tr><td>0.20<td>0.329
 <tr><td>0.25<td>0.464
 <tr><td>0.30<td>0.618
 <tr><td>0.35<td>0.811
 <tr><td>0.40<td>1.021
 <tr><td>0.45<td>1.259
 <tr><td>0.50<td>1.523
 </table>