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A Review of Vectors

A Review of Vectors. Vector Mechanics in the Game of Pool. Richard Damian Dimitry Hikin Wai Feng Xu SC441L New York City Technical College May 17, 2002. Overview. Review of Experiment Vector Terminology Vector Addition Data and Analysis Summary of Results Vectors in the Game of Pool

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A Review of Vectors

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  1. A Review of Vectors Vector Mechanics in the Game of Pool Richard Damian Dimitry Hikin Wai Feng Xu SC441L New York City Technical College May 17, 2002

  2. Overview • Review of Experiment • Vector Terminology • Vector Addition • Data and Analysis • Summary of Results • Vectors in the Game of Pool • Introduction to Pool • Application of Vectors in Pool • “Ride the Nine” Shot Analysis • Conclusion

  3. Vector Terminology • vector n. A quantity completely specified by a magnitude and a direction. • Velocity • Displacement • resultant n. A single vector that is the equivalent of a set of vectors. • equilibrant n. A vector equal and opposite to the resultant. • component n. One of a set of two or more vectors having a sum equal to a given vector.

  4. Vector AdditionGraphical Method • Graphical Method [first approach] • Place tail of vector B at the head of vector A • Resultant = vector from tail of A to head of B A R B A B E R

  5. Vector AdditionGraphical Method (cont’d) • Graphical Method [second approach] • Place tail of A1 with tail of B1 • Form a parallelogram • Duplicate vectors A1 and B1 to create A2 and B2 • Place tail of A2 at head of B1, tail of B2 at head of A1 • Resultant = vector from tail of A1 and B1 to head of A2 and B2 A1 A2 B1 R B2 A1 B1 E R

  6. Vector AdditionComponent Method • Component Method • x axis is labeled i • y axis is labeled j By j R A Ay j Ay j By j B Axi Bxi Axi Bxi Get the x and y values of A and B AxI, Ayj, BxI, Byj, Add x and y components E

  7. Data and AnalysisTrial 1

  8. Data and AnalysisTrial 2

  9. Data and AnalysisTrial 3

  10. Summary of Results • Graphical Method Percent Error • 1st Trial – 0.77% • 2nd Trial – 0.38% • 3rd Trial – 2.27% • Component Method Percent Error • 1st Trial – 0.38% • 2nd Trial – 6.03% • 3rd Trial – 1.95% • Sources of Error • Unbalanced force table • Strings touching edge of table – friction • Ring in center of table was not completely centered • Human error when setting balance

  11. Introduction to Pool • PoolisPhysics • The Pool Table

  12. Introduction to Pool (cont’d) • Pool Balls • Weight: 6oz or 170gm • Diameter: 2.14in or 5.7cm • Classification in Game • Numerical – 1-15 • Solids & Stripes • 1-7 Solids • 9-15 Stripes Standard Balls Elephant Beautiful Balls

  13. Application of Vectors in Pool • Cue-ball aim • Cue-ball and object-ball direction • Ball direction after hitting rail • Cue-ball placement • Object-ball positioning

  14. “Ride the Nine” Shot Cue ball to be hit at 45 degrees towards 1-ball to sink in side pocket, continue to hit 9-ball to sink in corner pocket

  15. “Ride the Nine” Shot (cont’d) Reverse angle of previous photo

  16. “Ride the Nine” Analysis • 1st Video – “Failed Shot.mpg” • Cue ball hit directly into 1-ball • No angle change • Resultant has same direction as cue and object ball • 2nd Video – “Successful Shot.mpg” • Altered direction of cue ball to slice 1-ball into side pocket • Cue ball travels down the rail to sink 9-ball into corner pocket • Analysis of Successful Shot • Vectors of cue-ball (after collision) = A • Vector of 1-ball (after collision) = B • A + B = R • Equilibrant is path that cue ball originated from

  17. Conclusion • Vectors have both magnitude and direction • Vectors can be added geometrically • Add x and y values of vectors to find resultant • Pool is a vector game • Vectors help players aim for shots • Magnitude and direction of ball movement determines stopping position

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