Mathematical Analysis Of Pool Table Geometry And Tangent/Normal Line Calculations

Preview 2 of 2 pages

See the first 2 pages exactly as they appear in the document.

Page 1
Read page 1 as text
Mathematical Analysis of Pool Table Geometry and Tangent/Normal Line Calculations 1) Since the pool table is 3.8 feet wide, the pocket to the right of the origin is located at the point (1.9,0). From the first diagram, it is easily determined that the pocket above the origin is located at the point (0,1.6) This gives us two equations that we can solve for a and b. 0 = b – a(1.9) 2 1.6 = b – a(0) 2 The second equation immediately yields the result b = 1.6. Solving the first equation for a gives 0 = 1.6 – a(1.9) 2 a = 0.4432 The equation of the parabola is then: y = 1.6 – 0.4432x 2 2) The slope of the line is defined as change in y divided by change in x. This becomes: (1.6 – 0.4432p 2 – 0) / (p – 0) (1/p)(1.6 – 0.4432p 2 ) 3) To find the slope of the tangent line, take the derivative of the function. slope tangent line = y’ = - 0.8864p
Page 2