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Measuring the Bounce of Tennis Balls

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IB Math Studies Project

Sami Abusada Ms. Horsington/ Mr. Nicholson

Candidate number:

IB Math Studies project

Introduction to the measure of the bounce of Tennis balls

Now days, most tennis balls brands such as Penn or Dunlop, release a variety of types of balls to give a different perspective to a tennis match depending on thematerial of the court. The ball consists of a circular shape of around 6.7 cm and has a soft fiber all around the outside of the color fluorescent yellow. Inside, it is basically hollow, but contains air or nitrogen pressure to make the ball bounce. Depending on the amount of pressure you add to it, the ball will bounce less or maybe more. For example, in a clay court, it is mostly common to use aball that has less air pressure inside to make it slower, due to the idea that players tend to slide in the clay. But if you play on a hard court, the ball will have more air pressure to make the ball faster and bounce higher. To prove these, I will use 2 different brands of balls, such as Dunlop and Penn (which I mentioned before), to see how the bounce on each ball differs from each other brandin the two selected types of courts for the experiment which are clay, and hard court. I will not go directly to the courts, but I will do it on cement to see if they really have less or more air pressure. Also, I would like to see if the outside material could maybe be thinner which also affects the bounce. In a mathematical way, I will prove everything by using percentage change, graphs,division and scatter plots to differentiate between the brands performance, and the measure of air pressure in both types of balls.

STATEMENT OF TASK:

In this project, I want to prove two different things. First, I want to prove how according to the type of ball (clay or hard-court) the ball bounces less when being used or new, and how both brands compare in types of balls to see which o thebrands has more quality in terms of how much the ball lasts its air pressure. I want to prove that the performance of the types of balls are right, according to what brands state, that for clay balls, the balls have less air pressure so that they can be slower, and hard balls have more air pressure to make the ball faster. To prove this, I will measure the percentage change for each of the 8 balls,and see how during the bounces they lose the air pressure and therefore it proves why they bounce less each time. I will measure the percentage of all the bounces including the initial bounce to see how it differentiates from the other balls.

RAW DATA COLLECTION:

Hard-court new Balls

|Brands |Bounce#1 |Bounce#2 |Bounce#3|Bounce#4 |
|Penn |56cm |30cm |25cm |8cm |
|Dunlop |54cm |32cm |22cm |6cm |

Hard-court used balls

|Brands|Bounce#1 |Bounce#2 |Bounce#3 |Bounce#4 |
|Penn |50cm |28cm |24cm |6cm |
|Dunlop |48cm |27cm |18cm |6cm|

Clay court new balls

|Brands |Bounce#1 |Bounce#2 |Bounce#3 |Bounce#4 |
|Penn |47cm |22cm |14cm |5cm |
|Dunlop |45cm |22cm...
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