Index Rationale: Purpose of the Underhand Serve: Speed ​​Calculation ExampleGraphs of Other ServesStanding FloatJump TopspinEquation modeling position versus time for the topspin jump:Modeling equation position versus time for the floating jump: Evaluate and compare serves Conclusion: Decide on the best serving method Rationale: This investigation will consider the dynamics of a volleyball after it has been served. The reason I chose this topic is because I love playing volleyball and I do it almost every day. Some time ago I suffered a back injury that prevented me from serving. Now that he's almost healed, I'll start serving again. Now that serving is an option for me, if I actually want to serve in a match, I have to prove to my coach that I can serve effectively. Some factors that greatly affect the effectiveness of a serve include how high the ball reaches, the time the receiving team has to reach the ball, and the speed of the ball. Say no to plagiarism. Get a tailor-made essay on "Why Violent Video Games Shouldn't Be Banned"? Get an Original Essay Purpose My goal is to determine the difference in the dynamics of a volleyball game when served using various methods. Serving methods include the underhand serve, standing topspin, standing float, jumping topspin, and jumping float. By filming my teammates' serves and analyzing the video footage using Logger Pro, I was able to create graphs that model the ball path for each type of serve.[*] The following image shows how I evaluated the serve placing a point where the ball is located in each frame of the video to create a Position/Time graph for an underhand serve. The image is just a snapshot of the process, so it's not a complete graph yet. Underhand Serve: Example Calculation An underhand serve is one in which the server holds the ball in one hand at waist height and hits the bottom of the ball with the other fist. This is a very simple serving method, but will serve as a good basis for comparison for the other serving types. Equation that models position versus time for sneaky: maximum height. This affects the difficulty of the serve, because the higher the ball goes, the easier it will be for the defender to reach it. Alternatively, this value could be found by finding the value for which the derivative of this function equals zero, because the ball is instantaneously at rest when it reaches its maximum height. Speed ​​The speed of the volleyball is an important aspect of how difficult a shot is. to serve is to receive; the faster the ball goes, the more difficult it will be for a defender to make an accurate pass. Speed ​​also affects the time the defender has to approach the ball, which will be evaluated later. To determine the vertical component of the ball's speed, you need to take the derivative of the Position versus Time graph (this graph only takes into account the vertical position, so taking the derivative will only give you the vertical component of the velocity). the velocity component of the ball when it is at a height of 3 feet will be evaluated. This height was chosen because it is the approximate height at which the opposing team's defense will make contact with the ball. Solve using the quadratic formula: The value by which the receiver of the serve will contact the ball cannot be negative, so the speed of the ball when the receiver passes it will be in seconds. The same goes for volleyball when the opposing team is therereceives is. The horizontal component of the velocity remains unknown, but can be calculated using trigonometry. The value for ? is unknown and can be calculated using the following formula where g is the acceleration due to gravity, v is the velocity resulting in , and is the time the ball remains in flight (the time it takes for the ball to hit the ground) . The following equation gives the value of atthe launch point, so the value can be directly substituted into the equation which will work, because the horizontal velocity does not change in this model. TimeAnother important factor in the effectiveness of a serve is the time the defending team has to reach and pass the ball after it has been served. There are two ways to measure this. The first is to simply calculate how long the ball stays in the air. This can be determined by finding the moment when the opposing team receives the ball. It has already been determined to amount to 1.82336 seconds. This assumes that the receiving team has full vision of the ball from the moment it is served and can immediately understand where the ball is going and move to that position. However, due to opposing players blocking the defense's view and possible confusion as to where the ball will actually land, especially if wind is a factor, it is extremely difficult for a defender to know where to go immediately when the ball is served. Therefore, a more accurate way to determine the time a defender can use to reach the ball is to find the length of time the ball remains in the air after clearing the net. This works because, even though the defender can see the ball before it goes over the net, he usually takes this time to figure out where it is going and starts moving after the ball goes over the net. This does not necessarily occur when the ball is at its maximum height, so the time that the ball has a horizontal displacement of 30 feet (this is the distance between the end of the court, where the volleyball is served, and the net).Displacement formula: We assume no horizontal acceleration of the ball, so the equation becomes. The time available to the receiver to approach the ball is the difference in time between when the ball passes over the net and when it is received: this time does not seem entirely correct, considering the fact that from the photo it seems that the ball crosses the net at a level that appears to be very close to the maximum height, which occurs at . What this tells me is that the horizontal speed must be wrong. I will continue to use these mathematical processes with my other types of serves and record the calculations, and I hope the results will help me determine what exactly caused the incorrect horizontal velocity.Graphs of other servesTopspin standing. The standing topspin is an overhead serve in which the server touches the ball with his hand about an arm's length above his head. The batsman snaps his wrist when he makes contact with the ball, giving the ball a forward spin, as indicated by the name. Standing Float A standing float serve is an overhand serve very similar to a standing topspin serve. The only difference is that instead of snapping the wrist, the server hits the center of the ball with a steady hand, which causes the ball to have little to no spin as it clears the net. Since it has no spin, air currents often cause the ball not to move along a directly straight path, making it appear as if it is "floating around". four-step approach and jump to hit the ball, snapping their wrist when they make contact with it. This movement is very similar to squashing the ball, which allows the!