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When the coefficient of restitution (COR) is <> 1, then the angle of reflection (Ar) is not equal to the angle of incidence (Ai). Instead, with COR = 0.7:
Tan (Ai) = COR * tan(Ar) .
This I because only the velocity directly in line to the impact is reduced by the COR; the velocity perpendicular to the rail is not affected. Using the notation in Part I:
x1/2s = 0.7 * x2/8s & (again)
x1 + x2 = 2s leads to
Ai = 8.472 deg, Ar = 12.011 deg, x1=.29787s and x2=1.70213s
The cue ball starting spot is 4 * x1 + x2 = 2.8936 s = 2.8936 rail sights from the target pocket.
From here, realizing that path length is slightly different from part I, and also taking into account that only the perpendicular portion of the cue ball velocity is reduced by the factor of 0.7 when it bounces off the foot rail, an initial speed of 4.8929 * s^.5 is required, or about 22% faster than for Part I. |
