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Transcript of Bouncing Ball
Bouncing Ballby: Christian Geiger, Justice Good, and Connor Leighton2nd Period Pre Calc5/14/14
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OverviewOur group was given the task of dropping a ball, and recording the change in distance it bounced each time until it stopped bouncing. We then had to graph the data that we found.
The independent variable is the time (t) in seconds, because time can go on forever, and does not depend on anything else.
The dependent variable is the height (ft) of the ball, because the height that the ball bounces depends on how much time has passed.
HEIGHT IN FEETTIME IN SECONDS1 FT2 FT0631245We encountered a problem during our test. At the very end of the graph, the data points shot up unexpectedly from zero to 2 feet. Although it did not change the equation, we believe that one of us accidentally moved our hand in front of the sensor when retrieving the ball. The highest part of the graph was 1.69 feet, and represented the height of the ball when we originally started. The lowest part of the graph was 0 feet, and represented the ball striking the ground (0 feet). The Ball Bounce program flipped the plot, because it measured the height of the ball from the floor, instead of measuring from the ground.
The plot looks like the ball actually bounced on the floor because as time went on, the height that the ball bounced grew smaller and smaller.
This can be represented as the decreasing height of the arcs on the graph, or Y-values.overTime.(X-values)
For some strange reason our data was deleted before we were able to move further on with our experience. Luckily, we did the experiment again and got points that were very similar to the previous points.
Our next task was to select one of the six, or so, individual bounces that made up the data on our graph. Following the steps on the sheet, we selected one individual bounce from the graph and plugged in its points in the L5 and L6 charts. The L5 served as the X list and the L6 as the Y list.The type of equation that we came up with for the selected bounce was a negative quadratic equation. This happened because the bounce on the chart formed an upside down arc, revealing the top of the bounce. The regression equation that we came up with was as follows:Y=-14.83x2 + 9.66x +0.01The Y-intercept of our equation was (0, -0.001). This proves that at zero seconds, the ball is at -0.001 feet of the floor. In the context of the experiment (and in real life) because the ball cannot go below the floor.The equation would change if we were to write it for a later bounce because the x and y values would decrease as the balls bounces became smaller and as its hits the ground faster.Our next task was to find the velocity of the ball versus the time. Using the stat plots, we used the L5 for out x list instead of L1, and also changed the window to better fit the graph
Velocity (ft/sec)Time (sec).22.214.171.124.126.96.36.199.50-.3-.6*The changes can be seen when comparing this graph to our earlier graph.*The highest point of the graph coincided with the highest velocity. When the graph was decreasing and approaching zero, that was when the ball was reaching the top of its bounce. When the ball was at its highest point of its bounce, it hit the x-axis (and 0ft/sec). The graph then dips downward towards the negative velocity. This was when the ball started accelerating downwards due to gravity. The lowest part of the graph was when the ball was at its maximum speed while falling.
Throughout the experiment, we encountered a few problems. First, our date was erased which resulted in re-testing of the experiment. Each test was made to replicate our original test. Secondly, in our first set of data, part of the graph did not fit. This was most likely due to human error when disturbing the sensor. Also we had trouble with getting the sensor to register the ball bouncing.
We learned that a bouncing ball will have positive and negative velocities over time. Also, the velocities will lessen over time as the ball loses momentum. We learned that a ball will have no velocity as it is reaching the top of its bounce, and for a brief moment it had no velocity. Furthermore, we discovered that a bouncing ball forms a decreasing sinusoidal graph and that each bounce is a quadratic regression.
If we could change anything while doing this lab over again, we would have to make sure that our arms and limbs are not in the line of the sensor when retrieving the ball. Also, we would be more careful when using data on our calculator, while also making sure nothing gets erased.
**Disclaimer: These pictures have nothing to do with Bouncing Ball lab**