We found the average velocity of the marble over second, which was 69 cm per second. We used this average velocity to determine the final velocity, which was 138 cm per second. We then plugged this into an equation for the acceleration of the marble, which turned out to be the same. We plugged these variables into the equation to find displacements. All we needed was the time. This was determined by plugging the velocity and displacement of the buggy into the equation to determine time for the buggy, which would be the same for the marble, so they would hit at the same time. That time was 0.73 seconds. We plugged that in to the displacement formula for the marble, and got that the marble had to start at 36.9 cm.
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