A white billiard ball with mass mw = 1.5 kg is moving directly to the right...

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Physics

A white billiard ball with mass mw = 1.5 kg is movingdirectly to the right with a speed of v = 3 m/s and collideselastically with a black billiard ball with the same massmb = 1.5 kg that is initially at rest. The two collideelastically and the white ball ends up moving at an angle above thehorizontal of θw = 30° and the black ball ends up movingat an angle below the horizontal of θb = 60°.

1)

What is the final speed of the white ball?
m/s

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2)

What is the final speed of the black ball?
m/s

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3)

What is the magnitude of the final total momentum of thesystem?
kg-m/s

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4)

What is the final total energy of the system?
J

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Answer & Explanation Solved by verified expert
3.7 Ratings (395 Votes)

Let the velocity of white ball is v(w) and velocity of black ball is v(b).

Apply the law of momentum conservation in X-axis:-

( 1.5 kg ). ( 3 m/s ) + 0 = ( 1.5 kg ) .v(w) . cos30* + (1.5 kg ).  v(b) . cos 60*

Simplify the equation

1.299 v(w ) + 0.75 v(b) = 4.5 ............... (1)

Along y- axis, the momentum conservation yields

( 1.5 kg ) . v(w) . sin30* = ( 1.5 kg ) . v(b) . sin60*

v(w) = 1.732 v(b) ........... (2)

Substitute (2) in equation (1)

1.299

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