We used the double exposure pictures to calculate the velocity of the cork stopper. To do so, we used the ruler in the picture measured the distance between the two corks (displacement or d).  We then calculated the time delay between the flashes using a fan of known frequency with a line on it.  We took a picture of the fan using the same methods we used to photograph the cork and used Geometer’s Sketchpad to calculate the angle between the two lines.  Then, using the frequency of the fan and the angle between the two lines, we calculated the time delay (t) between flashes.  Since the bottle was positioned so the cork fired vertically then the acceleration (a) is -9.81 m/s/s.  Using the experimental values for a, t, and d we were able to calculate v or final velocity using the following formula.

d=v*t+(1/2)*a*t²

     time delay = angle BAC/(360°*frequency) since we measured frequency to be 53.0 Hz using a stroboscope.

     time delay = 154°/(360°*53.0 Hz) = .00807 seconds.  We knew that we chose to use the correct angle (154°) instead of 360°-154° because the velocity value we got using 154° matched the values we got from our video analysis, where as the velocity we got using 360°-154° gave us a value that was extremely different.

     We calculated the time delay to be .00807 seconds and measured the displacement to be 0.17 meters.  Then, using the formula, we found the final velocity to be 21.1 m/s.  To give a better idea of how fast this really is, it converts to 47.1 mph.

     We also used high speed videos in order to determine the velocity of the cork.  We used a program called Tracker to track the vertical position of the cork over time. 

     We then used the data points from tracker and placed them into a graphical analysis file.  We fit the data with a quadratic regression in graphical analysis.

     Since the data points are vertical position vs. time, the slope of the graph at t = 0 (or the coefficient of t in the quadratic fit) is the initial velocity of the cork. On the graph, above, the slope or initial velocity is 2.128 cm/ms, which converts to 47.60 mph. Note that this is actually an initial velocity as contrasted to the average value of velocity given by the previous method.