Final answer:
To find the final speed of the cue ball in a billiards game, use the principle of conservation of momentum and break down the velocity into horizontal and vertical components.
Step-by-step explanation:
To solve this problem, we can use the principle of conservation of momentum. According to this principle, the total momentum before the collision is equal to the total momentum after the collision. We can use this principle to find the final speed of the cue ball.
Before the collision:
- Cue ball mass (m1) = 0.50 kg
- Cue ball initial speed (v1) = 1.9 m/s
- Billiard ball mass (m2) = 0.30 kg
- Billiard ball final speed (v2) = 1.3 m/s
- Angle of billiard ball's path (θ) = 32° clockwise from the cue ball's original path
To find the final speed of the cue ball, we can break down its velocity into horizontal and vertical components. The horizontal component of the cue ball's velocity remains unchanged after the collision, while the vertical component becomes zero. Using these components, we can calculate the final horizontal and vertical speeds of the cue ball. Then, we can find the final speed of the cue ball using the Pythagorean theorem.
The final speed of the cue ball is approximately 1.4 m/s.