Leisure or Hobbies: Application of Mathematical Terms

MATH5103 MR Application
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MATH5103 MR Application
One of my favorite pastimes and hobby is tennis: I like playing the sport because of its numerous mental and physical benefits. Tennis is played on a court divided into two halves by a net stretching across the center. It is not a team sport; therefore, there are no roles or positions. However, some games are played in doubles, and the team of two players must be constantly aware of each other's positioning to get their opponents off-guard. In tennis, a player volleys a ball from their side of the court, using a racquet, to the opponent's side of the court. The aim is to ensure that the other player does not volley the ball back before it bounces twice. If the ball bounces twice, a point is scored. Another point is gained if the opponent volleys the ball outside the playing area. A challenging problem in tennis is hitting the right angles: tennis is a game of strategy, and finding an angle inaccessible to your opponent is the best way to win. The aim, therefore, is to create wider angles that overwhelm your opponent.
Geometry is, therefore, a useful math concept in tennis since player positioning is central to creating broader angles and making it improbable for the opponent to volley back the ball without bouncing twice. Many commentators have suggested controlling the middle court as this is where the widest angles can be achieved. Geometrical concepts support this strategy and indicate that the player commanding the middle of the court has the advantage: positioning oneself in the middle court allows one to reach the opponent's volleys easily and also dictates the game. Three other mathematical concepts or essential ideas involved or related to the problem of controlling the middle of the court are the coefficients of kinetic friction, coefficient of the resolution, and powerful serve (Brody, 1997). All three ideas are based on elements of angles, distances, space, and speed. Ball spin is an essential factor in tennis since applying a correct topspin ensures that the volley is accurate without hitting the net. Top spins are especially favored because they are difficult for the opponent to catch: the opponent is more likely to mistime the ball because the ball drops down at the feet, making for a problematic offensive reply.
However, spin is influenced by ball-string friction when the leading strings of the racquet exert torque on the ball during impact. The tennis player must therefore wield the racquet in a manner as to create the best ball-string friction and maximize his or her topspin. The coefficient of restitution has to do with the post-impact velocity of the tennis ball after a serve or the energy lost after the ball hits the fixed surface of the racquet. Having a higher post-impact angular velocity is central to winning the game since the opponent is less likely to reach the ball or serve it back accurately. However, the...