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Two billiard balls of equal mass move at right angles and meet at the origin of an xy coordinate system. Ball A is moving upward along the y axis at vA = 2.3 m/s , and ball B is moving to the right along the x axis with speed vB = 3.5 m/s . After the collision, assumed elastic, ball B is moving along the positive y axis

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A.) What is the final direction of ball A?

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B.) What are their two speeds?

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Ball A is moving upwards along y-axis with a velocity of $\"\"$ .

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Ball B is moving upwards along x-axis with a velocity of $\"\"$ .

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Draw the coordinate system for the situtaion.

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$\"\"$

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Observe the figure:

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Conversation momentum along x-axis:

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$\"\"$

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Substitute $\"\"$ .

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$\"\"$

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Conversation momentum along y-axis:

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$\"\"$

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Substitute $\"\"$ .

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$\"\"$

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Conservation of kinetic energy:

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$\"\"$

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$\"\"$

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Substitute $\"\"$ and $\"\"$ .

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$\"\"$

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Step 2:

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Consider equation (1).

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$\"\"$

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Squaring on each side.

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$\"\"$

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Consider equation (2).

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$\"\"$

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Squaring on each side.

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$\"\"$

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Add equation (4) and (5).

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$\"\"$

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$\"\"$

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$\"\"$

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Substitute $\"\"$ .

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$\"\"$

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Since $\"\"$ cannot be zero then $\"\"$ .

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$\"\"$

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Substitute $\"\"$ in equation (1).

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$\"\"$

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Ball A moves with a velocity of $\"\"$ .

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Substitute $\"\"$ in equation (2).

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$\"\"$

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Ball B after collision moves with a velocity of $\"\"$ .

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As $\"\"$ , the ball A moves in the direction of x-axis.

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(b)

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From part (a):

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Ball A moves with a velocity of $\"\"$ after collision.

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Ball B moves with a velocity of $\"\"$ after collision.

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