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Homework Statement
A white billiard ball with mass mw = 1.53 kg is moving directly to the right with a speed of v = 3.25 m/s and collides elastically with a black billiard ball with the same mass mb = 1.53 kg that is initially at rest. The two collide elastically and the white ball ends up moving at an angle above the horizontal of θw = 51° and the black ball ends up moving at an angle below the horizontal of θb = 39°.
1) What is the final speed of the white ball?
Homework Equations
p=mv
k=0.5mv2
Vcm = (M1V1 + M2V2)/ (M1+M2)
The Attempt at a Solution
I don't really have any idea how to solve this.
I started by first finding the velocity of the center of mass:
Vcm = (M1V1 + M2V2)/ (M1+M2)
Vcm = (1.53*3.25 + 1.53*0) / (1.53 + 1.53)
Vcm = 4.9725/3.06 = 1.625 m/s
And the initial momentum: P1i = M1V1i = 1.53*3.25 = 4.97 kg*m/s
Since the collision is elastic, I know the final kinetic energy is equal to the initial, which means that K1f + K2f = K1i
K1f + K2f = 0.5M1V1i2 = 0.5(1.53)(3.252) = 8.08 J
Since momentum is conserved, I also know that the vertical momentum M1V1fy + M2V2fy = 0
And that the horizontal momentum of the two balls after the collision has to equal the initial momentum: M1V1fx + M2V2fx = 4.97 kg*m/s
In the CoM frame, the 2 balls collide and then head off at the same speed, but for the life of me I can't figure out how to transform the speed in the CoM frame (1.625 m/s for each ball) back to the original frame without knowing what angle they are moving at after the collision in the CoM frame. And I don't know how to get the angles in the CoM frame from the angles in the original frame.