While shooting pool, you propel the cue ball at a speed of 1.20 m/s. It collides

Question

While shooting pool, you propel the cue ball at a speed of 1.20 m/s. It collides with the 8-ball (initially stationary), propelling the 8-ball into a corner pocket. The cue ball is deflected by 40.0 degrees from its original path by the collision, and it moves away from the collision with a speed of 0.800 m/s. The goal of this exercise is to determine the magnitude and direction of the 8-ball’s velocity after the collision. The cue ball has a little more mass than the 8-ball, but assume for this exercise that the masses are equal.

Let's define the direction of the cue ball's velocity before the collision to be the x-direction, and we can also say that the velocity of the cue ball after the collision has a positive x component and a positive y component.

(a) Calculate the x-component of the 8-ball's velocity after the collision. Use a positive sign if the x-component is positive, and a negative sign if the x-component is negative.
1___________m/s

Explanation / Answer

conserving momentum in y -direction,

0 = m*.8*sin40 - m*v*sin

so, v*sin = 0.514

conserving momentum in x-direction,

m*1.2 + 0 =m*.8*cos40 + m*v*cos

so, v*cos = 0.587

so, tan = 41.2 degrees

so, v = .514/sin41.2  =0.78m/s

so the x-component of 8-ball's velocity = v*cos41.2 = 0.587 m/s

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