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The Calculus of Juggling

The Calculus of Juggling. Ashley Bennett Stephen Bent. 3-Ball Cascade. 5-ball Cascade. We knew that the formula for an accelerating body is:. Distance = (startingvelocity)(time) +(1/2)(acceleration)(time)(time) d = (v o )(t)+(1/2)(a)(t 2 ).

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The Calculus of Juggling

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  1. The Calculus of Juggling Ashley Bennett Stephen Bent

  2. 3-Ball Cascade 5-ball Cascade

  3. We knew that the formula for an accelerating body is: Distance = (startingvelocity)(time) +(1/2)(acceleration)(time)(time) d = (vo)(t)+(1/2)(a)(t2)

  4. Second Degree Taylor Polynomial General Formula: P2(x) = f(a) + f’(a)(x-a) + ½f’’(a)(x - a)2 Specifically: d = (first derivative) (change in time) + (½) (second derivative)*(change in time)* (change in time)

  5. Height Hand 1q1 Hand Three Ball Cascade: t/2 = .496/2 = .248 seconds Five Ball Cascade: t/2 = .658/2 = .329 seconds

  6. Three Ball Cascade: d = (0)(.248) + (1/2)(9.8)(.2482) = .30317 meters • Five Ball Cascade: d = (0)(.329) + (1/2) (9.8) (.3292) = .53038 meters

  7. 3 Ball Cascade 5 Ball Cascade

  8. V = V0 + a*t • Three Balls: V = (0) + (9.8) (.248) = 2.4304 meters/second • Five Balls V = (0) + (9.8) (.329) = 3.2242 meters/second

  9. Three Balls:V = V0 + (a) (t) V = 2.4304 – (9.8*t)

  10. Five Balls:V = V0 + (a) (t) V = 3.2242 – (9.8*t)

  11. Assumptions • 1: Juggling is consistent • 2: Gravity is the only force • 3: Stephen’s juggling height and speed is law!!!

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