the answer is provided please show me in details how to arrive at it You are pla
ID: 1557306 • Letter: T
Question
the answer is provided please show me in details how to arrive at it
You are playing billiards. There are two billiard balls left on the table (balls B and C), each having a mass of 200 grams. Both balls B and Care initially at rest and next to the edge of the table. Your cue ball, ball A, also has a mass of 200 grams. Your goal is to get Ball C into the pocket shown. You strike the cue ball, A, so that it travels at the angle and velocity indicated in the figure. Cue ball A strikes ball B. Determine the following: What would ball B's velocity (in terms of x and y components) be after the collision with ball A? This assumes that Ball B was not next to the edge of the table. (Answer: -1.644 m/s and -0.599 m/s) Will ball B hit ball C? If so, will ball C have enough velocity to fall in the pocket after getting hit by ball B? Provide assumptions and calculations to support your answer. Assume that the coefficient of restitution is e = 0.75.Explanation / Answer
We can resolve the velocity of the cue ball in x component as 2 cos 20 = 2 x 0.94 = 1.88 m/s
and the y component of the velocity of the cue ball as 2 sin 20 = 2 x 0.34 = 0.68 m/s
Then we can take that in the x axis the ball B (which is at rest) is struck by ball A with a velocity UA= 1.88 m/s.
We define UA and UB as the inititial velocities of ball A and B and VA and VB as their respective final velocites
By law of conservation of momentum mUA +mUB = mVA + mVB
We get UA + 0 = VA + VB as all masses are equal. This gives 1.88 = VA + VB .............(1)
By law of conservation of momentum we get (VA-VB) / (UA-UB) = COR = 0.75 given
So VA-VB = 0.75 x (UA-UB) From this we can get VA-VB = 0.75 x UA = 0.75 x 1.88 = 1.41
Or in other words VA-VB = 1.41..................................................................................(2)
Adding (1) and (2), we get 2 VA = 3.29 Or VA = 1.644 .
The direction is to the left of x axis and hence VA = -1.644 m/s Ans.
We can proceed similarly taking the y axial component of the velocity of the cue ball 2 sin 20 = 2 x 0.34 = 0.68 m/s and the coefficient of restitution COR as 0.75, find out the VA in y axis.
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