Math and Graph Models Behind the Olympic Paul Vault Jump
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Every 4 years, the Olympic games is a major event around the world. International athletes come together to represent their own country at a sport. A gold medal is given to the winner of each game. This math internal assessment aims to consider the trends of the wining men gold medalist’s pole vault height from 1932 to 2008, and predicting 1940 and 1944 record, when the Olympic games were not held due to the world war.
Data – Height Record 1932-2008
The table below shows the men pole vault gold medalists at various Olympic games between 1932 and 2008.
Table 1: the winning heights of men’s pole vault in Olympic games for years between 1932 and 2008. (Excluding 1940 and 1944)
Year 1932 1936 1948 1952 1956 1960 1964 1968 1972…show more content… The war, however, stopped the improvement of the heights record. Therefore, we could deduce that the depression between 1936 and 1948 was due to lack of training due to the war. When the games resumed in 1948, the athletes started to progress their record once again.
As you can see above, we could refine our model, disregarding the 1932 and 1936 record.
Graph 5: Graph of winning heights (m) against years since 1948
This refined model is better representation of data than graph 1 and 2 even if the line does not pass through every point. Passing through point increased from 2 to 3 (4, 52 and 56) and majority of points are very close to the line. It is true that some points, such as point 16 and 20 quite far from the line, but these points can be disregarded in this model, as the line is touching the following point 24.
This gives the new linear equation y=0.0264x+4.4338 However, even though refined graph has better equation than those of past one, there are some limitations with using linear equation to determine the graph. Since a linear graph increases infinitely, and as humans have restraints to achieve to record, their winning height can’t keep increasing at this rate. It is not sustainable. Natural Logarithm Model
After considering the limitation of linear function and graph, I have discovered applying any model of equation that has an infinite increase range, such as quadratic or exponential, is unrealistic, since the