Bouncing Ball by: Christian Geiger, Justice Good, and Connor
Leighton 2nd Period Pre Calc 5/14/14 Thats one focused
player>>
Slide 2
Overview Our 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.
Slide 3
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.
Slide 4
HEIGHT IN FEET TIME IN SECONDS 1 FT 2 FT 06 31 2 4 5
Slide 5
We 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.
Slide 6
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).
Slide 7
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. over
Time.(X-values)
Slide 8
*Disclaimer!* 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.
Slide 9
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=-14.83x 2 + 9.66x +0.01 The
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.
Slide 10
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
Slide 11
Velocity (ft/sec) Time (sec).3.6.9.6.3.1.2.4.5 0 -.3 -.6 *The
changes can be seen when comparing this graph to our earlier
graph.*
Slide 12
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.
Slide 13
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.
Slide 14
The End **Disclaimer: These pictures have nothing to do with
Bouncing Ball lab**