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A cue ball of inertia m is given a speed v before it collides elastically with a full rack of 15 stationary balls in a game of pool. Each of the 16 balls has an inertia m.

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onyebuchinnaji

The final speed of the 15 stationary balls in a game of pool is determined as the ratio of inertia of the cue ball to total mass of the 15 balls.

Final speed of the 15 balls

The  final speed of the 15 balls can be determined by applying the principle of conservation of linear momentum as shown below;

J = ΔP

where;

  • J is inertia
  • ΔP is change in momentum

m1u1 + m0u0 = m1v1 + m0v0

where;

  • m1 is mass of the cue ball
  • m0 is mass of the 15 balls
  • u is initial velocity
  • v is final velocity

m1u1 - 0 = m1v1 + 15mv0

m1u1  - m1v1 = 15mv0 - 0

recall, m1u1  - m1v1  = ΔP = J

-m = 15m0v0

v0 = -m/15m0

where;

  • v0 is the final speed of the 15 balls
  • 15m0 is the total mass of the 15 balls
  • m is the inertia of the cue ball

Thus, the final speed of the 15 stationary balls in a game of pool is determined as the ratio of inertia of the cue ball to total mass of the 15 balls.

Learn more about linear momentum here: https://brainly.com/question/7538238

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