please show work and do not round answers!: A white billiard ball with mass m w
ID: 1475762 • Letter: P
Question
please show work and do not round answers!: A white billiard ball with mass mw = 1.34 kg is moving directly to the right with a speed of v = 3 m/s and collides elastically with a black billiard ball with the same mass mb = 1.34 kg that is initially at rest. The two collide elastically and the white ball ends up moving at an angle above the horizontal of w = 34° and the black ball ends up moving at an angle below the horizontal of b = 56°.
1) What is the final speed of the white ball?
2) What is the final speed of the black ball?
Explanation / Answer
momentum conservation
about x-axis
mw*v + mb*0 = mw*Vw*cosw + mb*Vb*cosb
=> 1.34*3 = 1.34*0.82903757*Vw + 1.34*0.5591929*Vb
=> 1.111*Vw + 0.75*Vb = 4.02 ............. (1)
about y-axis
0 = mw*Vw*sinw - mb*Vb*sinb
=> Vw*0.75 = 1.111*Vb
=> Vw = 1.4813*Vb
put in eq 1
=> 1.111*1.4813*Vb + 0.75*Vb = 4.02
=> Vb = 1.6785 m/s
=> Vw = 2.486 m/s
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