# Uncertainties in timing a tennis ball hitting the ground

In a group of four, the aim was to record the time of a tennis ball being dropped from a certain point on the third floor of the Great Portland Place school campus until it hit the ground of the ground floor; and then record the uncertainties of the experiment. In this experiment the following apparatus was used;  two stopwatches which measures to 2 decimal places (1/100 of a second – centiseconds) 4 ordinary tennis balls  Utensils to record the time of each tennis ball try There was 21 tries done using 4 different tennis balls, in order to gain sufficient data to provide a measurement of time taken. In order to improve the accuracy of the time of one try, time was recorded from the third floor and the ground floor simultaneously. These measures were all mainly relied upon our auditory and visionary perceptions.The results collected was then be used to calculate the most accurate gauge for a tennis ball being dropped from the third floor of the Great Portland Place campus until it hits the ground, without ignoring the inaccuracies which occurred during the experiment.

The measures recorded from the ground and Third floor were combined to create a big set of data. The data is sorted in ascending order. The average of all these times is approximately 1.28 seconds.

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The lowest measure (1.12 sec) is 0.16 seconds below the average, while the highest measure (1.

65 sec) is 0.37 seconds above the average. The average of these two is approximately 0.27 seconds and so the time could be written as 1.28 ï¿½ 0.27 seconds.This is a way which is too broad and imprecise in trying to find an accurate measure. There needs to be refinement in the data because if one looks at the data of the times measured from the third and ground floor one will find that there are many random errors with too many measures which are too big and too small.

These errors in timing were most likely caused by the person’s reaction when timing. These errors can be easily be deciphered on a graph (next page).These errors increase inaccuracies of the final result and therefore the data has to be reduced to a more accurate set of data. The best way to eliminate errors is by downsizing the number of data to the measures found between the lower and upper quartile (divides the data into four). The lowest measure of this set of data (1.22) is 0.05 sec below the average, while the highest measure of this set of data (1.

34) is 0.07 sec above the average.The average of these two is 0.06 sec and so the time could be written as Looking at the graph of the manipulated data it looks like there are still some random errors in these measures and the average 1.27 has an uncertainty of ï¿½ 0.06 sec. which is still not the most accurate result possible to get. So the same process which was done to find the first manipulated data will be done again.

In order to refine this manipulated data the quartiles need to be found again. There are 27 numbers so therefore the median is in 131/2 place: median = 1.27 approx. The lower quartile is approximately 1.

23 and the upper quartile is approximately 1.28. So therefore in this second manipulated data there will be numbers between 1.23 seconds and 1.

28 secondsTennis ball dropping tries Times measured from the ground and third floor (seconds) Uncertainties for measurement of time is decided when a measurement is too big or too small to the other data. Most of the causes of the errors which gave anomalous results are most likely the cause of the human reaction when timing a ball. A human will rely mostly on its auditory and visionary perception during such an experiment. The speed of light is much faster than the speed of sound therefore one should rely more on one’s sight during such an experiment but hearing the impact of the ball on the ground is the signal that one would instinctively wait for before stopping the stopwatch. Therefore this means there will be more inaccuracies if one depends mostly on the auditory perception than on the vision.

During the experiment some of the students dropped the ball before the given signal or they stopped the stop watch before the ball hit the ground. The position of the ball (although the ball was set at a certain point on the third floor) might change by a few millimetres changing the distance of the ball’s flight in a tiny way. The stopwatch since it measured to the 1/100 of a second was a strong inaccuracy for this kind of experiment.

These kind of experiments which measures precise spaces of times less than 30 seconds are not very helpful when using a stopwatch, and it is better to use an electronically watch. The results are very inaccurate using a stopwatch because there are many errors caused mainly by the person’s reaction-time. When narrowing down my data the uncertainty decreased as well, this therefore means that my technique of manipulating my data was successful. All I did is to keep subtracting all the anomalous data from the previous data. I f I had continued the process I would have gotten and even more precise answer with an uncertainty of ï¿½ 0.01 seconds. Still that answer would still not be fully accurate.