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For an elastic collision between two equal masses where one starts at rest, if neither the trivial head-on stop nor the no-collision case applies, what angle does the source say typically separates the two objects' final velocities, as seen in billiards?
AAbout 90 degrees
BAbout 30 degrees
CAbout 180 degrees
DAbout 45 degrees
Answer & Solution
Correct answer: A. About 90 degrees
1. For two equal masses in an elastic collision with one initially at rest, the source derives a term that must equal zero for the equations to be consistent.
2. One way to satisfy that condition is for the angle of separation between the final velocities to be 90 degrees.
3. In real pool and billiards play, the angle between the balls after a collision is very close to this value.
4. The other trivial ways to satisfy the equation are the incoming ball stopping completely or missing entirely, not a separation angle of 30, 45, or 180 degrees.
_Source: OpenStax College Physics (CC BY 4.0), Ch 8 "Linear Momentum and Collisions", section 8.6 Collisions of Point Masses in Two Dimensions_
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