In Figure P11.51, a cue ball is shot toward the eight-ball on a pool table. The cue ball is shot at the eight-ball with a speed of 8.00 m/s in a direction 30.0° from the y axis. Both balls have the same mass of 0.170 kg. After the balls undergo an elastic collision, the eight-ball travels in the negative x direction into the side pocket. What is the velocity of the cue ball after this collision?
FIGURE P11.51
The velocity of the cue ball after the collision.
Answer to Problem 51PQ
The velocity of the cue ball after the collision is
Explanation of Solution
Given that the speed of the cue ball is
From the given Figure, deduce the
Here,
Write the expression for the momentum conservation along
Here,
Since the eight ball has no final
Apply the conservation of kinetic energy to the collision process.
Reduce equation (VII).
Conclusion:
Substitute
Substitute
Substitute
Substitute
Substitute
Use equation (IX) in (XI) and solve for
The solution for
Substitute
Write the expression for the velocity of the cue ball after the collision.
Substitute
Therefore, the velocity of the cue ball after the collision is
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Chapter 11 Solutions
Physics for Scientists and Engineers: Foundations and Connections
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