Preveina from Crest Girls' Academy sent us some
thoughts:
I managed to fit a curve to the data. However when I tried
generating new values it didn't fit within my curve so I had to
draw another curve which fitted most of the points.
By using this graph you could answer scientific questions
like:
Are there any anomalous results being produced?
What relationship can be described between the variables using the
graph?
When does the graph reach its peak?
Herschel, from the European School of Varese sent
us a well thought out solution:
When the complete set of data is plotted on a graph, it appears as
three inverted parabolas, each in the general form $y =
-ax^2+bx+c$. It suggests an object such as a bouncing ball, with
the data showing its displacement or height.
The ball clearly bounces twice - once at about 0.65 seconds
and again at around 1.25 seconds - and it loses height each
time, due to the loss of kinetic energy at the point of impact. The
drastic loss of energy with each successive bounce suggests that
the surface is soft (such as carpet or grass) and that the ball is
a (slightly deflated) football rather than a bouncy ball.
The ball or object starts from a height of 206 at the start, and
it then reaches 47 after the first bounce and 15 after the third.
If we assume these values to be in centimeters, we can work out the
speed of impact on each of the third bounces with the formula
$v=\sqrt{2gh}$, without accounting for air resistance. We see that
the velocity upon the first impact is $6.35ms^-1$, $3.04ms^-1$ upon
impact for the second time and $1.71ms^-1$ the third time - in
other words, it loses half its speed each time it bounces.
We can also guess that it will reach a height of around 4cm after
the 3rd bounce and around 1cm after the fourth, since the maximum
height each time is approximately $\frac{1}{4}$ of the previous
time - 75% of the ball's energy is lost in the form of sound and
heat every time it bounces.
The graph plots height against time (i.e. the given data). There is
also derived data, namely (downwards) velocity and acceleration.
The original data (height) is on the right vertical axis while the
derived data (velocity and acceleration) is on the left vertical
axis, due to the difference in magnitudes of the values. Looking at
the basic data, we see that the height curve is quite smooth, and
the derived data shows that there is in fact a constant
acceleration throughout the experiment, with the exception of the
two points where the ball hits the ground and bounces. This is
expected if it is a bouncing ball - it is under the constant force
of gravity throughout the experiment.
A
lovely analysis, Herschel - it was in fact a small plastic cube
being dropped onto the carpet!