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Topics: Tennis, Serve, Newton's laws of motion Pages: 4 (735 words) Published: April 16, 2014
Mathematical exploration
Modelling of a tennis shot

Rationale:
I have decided to carry through my mathematical exploration on the topic of sports specifically tennis. When I first heard of mathematical explorations, I thought that it must be done on mathematical concepts such as algebra, number theory, geometry, probability and many more. However, after researching for some time I realized that what I do almost every week has a lot of mathematics involved in it. I am interested in tennis serve because I love playing tennis and it is something that I would like to know more of. An average male professional tennis player’s groundstroke is at an average speed of 70mph or about 112km/h (Tennis Serving Speed Male vs Female, n.d.). At this speed, the opponent will only have less than 1s to react. (How To See A 130 MPH Tennis Serve, n.d.). To be able to react to the shot we must be able to accomplish the three levels of response for interceptive timing tasks. First, there is the basic reaction or optomeric reaction which is seeing the ball and getting out of the way. Second, there is perceptual reaction which means you can identify the object that is coming at you and can put in some context whether it’s a ball or something else. Third, there is the cognitive reaction, meaning you know what is coming at you and able to react which in this case returning the 112km/h shot. Professional tennis player are at expert cognitive reaction through rigorous training. So, I have chosen to explore on tennis force with no air resistance acting on it and air resistance acting on it.

Introduction

Tennis is one of the most popular sports in the world but what do we know about it besides two or four people hitting the ball to each other. This exploration is written to develop a model of a tennis shot. For this exploration to work, I must find the factors that affects the motion of a tennis ball in the air. As the force exerted by every person is different, the velocity of...
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