# EE on Mathematics of Table Tennis

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Long Post

I am in Year 1 taking Mathematics as my subject for the extended essay. Initially i decided to use rotation of conic sections as my topic for my EE but i decided to change my topic again right before my IRS is needed (bc i dont feel motivated anymore on the old topic). Now, i am still trying to think of a new topic so that i can start writing next year. So far i read a Sample EE that garnered 32/36 points. It is about optimizing the distance of the kick of a ball from the conversion point to the try line in rugby considering only the plane parallel to the ground. The EE was easy to understand and as it simply defined the diagram and applied trigonometry, functions, and calculus(derivative) to look for the optimal distance and angle. Along with this method, he also used Circle theorems to achieve the same result.

This EE kind of inspired me because it is simple yet his investigation is profound and he had a lot to discuss. Because of this, i thought of switching to the topic of applying maths in sports. One of my considerations is soccer or football as it is closely related to rugby as well as ice hockey since it doesnt deal much with gravity, but alas i dont play soccer, football, or ice hockey so it may not benefit me to look into this (but i am willing to look into these if it is simpler)

Another one is table tennis where i thought of looking into the finding the range of angles wherein when hitting the ball, it would land and the maximum location(edges of the table) or near the net. One problem i encountered with this problem is that there are multiple variables regarding defining where the farthest and shortest trajectory of the ball with respect to the racket, how i hit the ball: angles along x and y, position of ball on the table, height where i hit the ball, gravity, spin on the ball, velocity etc. Last problem is how i will pattern this as a math EE as physics concepts are used here as well (projectile motions, angle of incidences etc).

in short, id like to ask your insights and possible remedies to my problem on

1. Concepts in sports where i can apply mathematics

2. How to deal with the plethora of variables that can be seen in the topic

3. math concepts i can use to tackle it the table tennis problem

4. how to tackle the physics here mathematically, any advice

Hope you guys can help, im sorry for the long backstory and the very demanding questions.

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