4. In a game of pool the cue ball hits the 9-ball, then he 9-ball hits the 11-ba

Question

4. In a game of pool the cue ball hits the 9-ball, then he 9-ball hits the 11-ball. The cue ball had a velocity of 6.1 m/s prior to hitting the 9-ball and no velocity afterwards. The 9-bal ends up moving with a speed of 3.4 m/s at an angle of 23° to the left of the cue ball's initial velocity vector after hitting the 11-ball. The cue ball has a mass of 170 g while the other balls have masses of 156 g. If we ignore drag and friction forces, what is the velocity vector of the 11-bal after it is hit by the 9-ball?

Explanation / Answer

4. Applying momentum conservation for collision,

pi = pf

(170)(6.1)i + (156 x 0) + (156 x 0) = (170 x 0) + (156)(3.4)(cos23i + sin23j) + (156)v

1037i = 488.3i + 207.2j + 156 v

v = 3.52i - 1.33 j m/s

Speed = sqrt(3.52^2 + 1.33^2) = 3.76 m/s

direction = tan^-1(-1.33/3.52) = - 20.7 deg  

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