A white billiard ball with mass m w = 1.61 kg is moving directly to the right wi

Question

A white billiard ball with mass mw = 1.61 kg is moving directly to the right with a speed of v = 3.03 m/s and collides elastically with a black billiard ball with the same mass mb = 1.61 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 = 54° and the black ball ends up moving at an angle below the horizontal of b = 36°.

1)

What is the final speed of the white ball?

m/s

Your submissions:

2)

What is the final speed of the black ball?

m/s

Your submissions:

3)

What is the magnitude of the final total momentum of the system?

kg-m/s

Your submissions:

4)

What is the final total energy of the system?

J

Explanation / Answer

a)
Apply conservation of momentum in y-direction

0 = mw*Vw*sin(54) - mb*Vb*sin(36)

mb*Vb*sin(36) = mw*Vw*sin(54)

1.61*vb*sin(36) = 1.61*vw*sin(54)

Vb = 1.376*Vw

now, Apply conservation of momentum in x-direction

mw*3.03 = mw*Vw*cos(54) + mb*Vb*cos(36)

3.03 = Vw*cos(54) + 1.376*Vw*cos(36)

3.03 = 1.7*VW

==> Vw = 3.03/1.7

= 1.78 m/s

b) Vb = 1.376*1.78

= 2.45 m/s

c) final total momentum = initial total momentum

= 1.61*3.03

= 4.88 kg.m/s

d) KEf = 0.5*mw*VW^2 + 0.5*mb*Vb^2

= 0.5*1.61*(2.78^2 + 2.45^2)

= 11.05 kg.m/s

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