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Ping-Pong

Ping-Pong. The Perfect Shot. Created by Ensar Tota and Evan McEllhenney of 8-3 Parabola Project. What is Ping-Pong?.

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Ping-Pong

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  1. Ping-Pong The Perfect Shot Created by Ensar Tota and Evan McEllhenney of 8-3 Parabola Project

  2. What is Ping-Pong? • Ping-pong, or table tennis is a sport or hobby that requires hand-eye coordination and skill.  The key point in ping-pong is for a person to serve the ball with a ping-pong racquet to make sure the ball bounces on his or her side and the opponent's side.  The returning ball is only allowed to hit the opponents side, or else it would be your opponent's point if you fail to complete so.

  3. There are Rules • ScoringA match is played best 3 of 5 games (or 4/7 or 5/9). For each game, the first player to reach 11 points wins that game, however a game must be won by at least a two point margin. A point is scored after each ball is put into play (not just when the server wins the point as in volleyball). The edges of the table are part of the legal table surface, but not the sides. • Flow of the MatchEach player serves two points in a row and then switch server. However, if a score of 10-10 is reached in any game, then each server serves only one point and then the server is switched. After each game, the players switch side of the table. In the final game (i.e. 5th game), the players switch side again after either player reaches 5 points. • Legal ServiceThe ball must rest on an open hand palm. Then it must be tossed up at least 6 inches and struck so the ball first bounces on the server's side and then the opponent's side. If the serve is legal except that it touches the net, it is called a let serve. Let serves are not scored and are reserved. • EquipmentThe paddle should have a red and a black side. The ball should be either orange or white and 40 mm in size. The table should be 2.74 meters long, 1.525 m wide, and 0.76 m high. (Courtesy of http://www.pongworld.com/more/rules.php)

  4. Our Mission • In our project, we are trying to find the perfect shot to make the ball just slightly touch over the net to make the ball rapidly bounce on the opponent's side.  Remember, the ball is only allowed to bounce once on a side, and failed to complete this will result in the opponent to earn a point.

  5. Graph

  6. First trial

  7. First Trial - Math Plug into the form of a(x)^2+b(x)+c=f(x) Simplify = = -1 X = f(x)=(-0.13)x^2+(-0.63)x+0.76

  8. First Trial – Quadratic Formula • Plug into Quadratic Formula Equation • f(x)=(-0.13)x^2+(-0.63)x+0.76 x=-b(+/-)b^2-4ac 2a x=-(-0.43)+(-0.43)^2-(4)(-0.08)(1.5)               2(-0.08) = x=-(-0.43)+(-0.43)^2-(4)(-0.08)(1.5)               2(-0.08) = x=0.43+0.1849-0.48             -0.16 = x=0.43-0.1849-0.48             -0.16 = = = x=0.1349     -0.16 x=-0.2349       -0.16 x=1.468 x=-0.843125

  9. First Trial – Vertex Form • f(x)=-0.13x^2-0.63+0.76 •     -0.13(x^2-0.63x)+0.76 •     -0.13(x^2-0.63x+0.5776)+0.76+0.13(0.5776) •     -0.13(x-0.63)^2+0.835088 • The vertex is ≈ (-0.63,0.83)

  10. Parent graph v. equation 1 • A in the equation -0.13x^2-0.63x+0.76 is negative, therefore the entire graph is upside • down compared to the parent graph x^2. • A is fairly small, which means the total span is short. • B is negative, therefore the graph moved 0.63 to the left. • C is 0.76, which means the entire graph rose 0.76 up on the y-axis.

  11. Second Trial

  12. Second Trial - Math Plug into the form of a(x)^2+b(x)+c=f(x) Simplify = = -1 X = f(x)=(-0.08)x^2+(-0.43)x+1.5

  13. Second Trial – Quadratic Formula Plug into Quadratic Formula Equation • f(x)=(-0.08)x^2+(-0.43)x+1.5 x=-b(+/-)b^2-4ac 2a x=0.63+(0.63)^2-(4)(-0.13)(0.76)                     2(-0.13) = x=0.63-(0.63)^2-(4)(-0.13)(0.76)                     2(-0.13) = x=0.63+0.3969-0.3952             -0.26 = x=0.63-0.3969-0.3952             -0.26 = = = x=-0.6317      -0.26 x= -0.1621      -0.26 x=0.62346 x=2.4296

  14. Second Trial – Vertex Form • f(x)= -(0.08) x^2 - 0.42 x + 1.5 •     -0.08(x^2-0.42x)+1.5 •     -0.08(x^2-0.42x+0.1764)+1.5+0.08(0.1764) •     -0.08(x-0.42)^2+1.514112 • The vertex is ≈ (-0.42,1.5)

  15. A is negative, therefore the graph is flipped upside down. • A is very small, which means there is a vertical compression or a horizontal • stretch, making the graph longer in terms of the x-axis. • B is -0.43, which means the entire graph moved 0.43 to the left. • C is 1.5, meaning that the entire graph rose 1.5 in terms of the y-axis.

  16. Third trial

  17. Third Trial - Math Plug into the form of a(x)^2+b(x)+c=f(x) Simplify = = -1 X = f(x)=(-0.5185)x^2+(-2.925)x+0.592

  18. Third Trial – Quadratic Equation f(x)=(-0.5185)x^2+(-2.925)x+0.592 Plug into Quadratic Formula Equation x=-b(+/-)b^2-4ac 2a x=2.925+(-2.925)^2-(4)(-0.5185)(0.592)                         2(-0.5185) x=2.925-(-2.925)^2-(4)(-0.5185)(0.592)                         2(-0.5185) x=2.925+8.556+1.227            -1.037 = x=2.925-8.556+1.227            -1.037 = = = x=12.708     -1.037 x=-4.404     -1.037 x=4.2469 x=-12.25458

  19. Third Trial - Vertex • f(x)=(-0.5185)x^2-2.925x+0.592 •     -0.5185(x^2-2.925x)+0.592 •     -0.5185(x^2-2.925X+8.555625)+0.592+(-0.5185)(8.555625) •   -0.5185(x-2.925)^2-3.844091563 • The vertex is ≈ (-2.9,3.8)

  20. A is negative, therefore the entire graph is flipped over. • A is -0.5, which is not that small compared to the other equations, so this • will have a higher maxima. • B is -2.9, which means the entire graph moved 2.9 to the left. • C is roughly 0.6, which means that the entire graph moved 0.6 up on the • y-axis.

  21. The Best Parabola Best parabola that will go just over the net.

  22. Math Behind the Shots Math Behind the Shots? • Okay, what we do is using the grid on slide 5, we figure out the coordinates on the graph. We then graphed them these using GeoGebra.  From there we used the points and translated them into a tangible equation! We plug those points into the standard form equation ax^2+bx+c=y. We take the three equations and turn them into matrices. Points a, b, and c are all a 3x3. The numbers on the opposite side of the equal sign become a 3x1 matrix. We then multiply the inverse of the 3x3 matrix by the 3x1 matrix. The result, our a, b, and c for our standard form of a quadratic equation. What is the connection between our project and parabolas?  Find a resource that shows the connection, name the resource, and tell the connection. • The trajectory of the ball is affected by two different forces. After being hit its horizontal velocity is constant. The ball’s vertical velocity increases because gravity causes it to accelerate downwards. These two forces combine to form a curved path or a parabola. (Holt Physical Science p. 358) The Biggest Challenge of our Project Was • Not filming the shots; or figuring out the math. It was assembling and synchronizing the information so that It was comprehendible. Putting everything together provided to be difficult but rewarding!

  23. Real World Connections • Parabolas are used in many different situations through out life. Parabolas are used in Satellite dishes which relay information when the waves bounce off the curved part of the dish. The Golden Arches are also Parabolas! Also don’t anger leprechauns otherwise the put of gold under the rainbow (parabola) will disappear! Smile!

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