In the figure below, 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 7.85 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? (Express your answer in vector form.) Vf, cue m/s 8 30°

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Chapter1: Units, Trigonometry. And Vectors
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The image depicts a pool table scenario involving a collision between a cue ball and an eight-ball. Here's the content as it might appear on an educational website:

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### Physics Problem: Elastic Collision on a Pool Table

**Problem Description:**

In the diagram shown, a cue ball is directed towards the eight-ball on a pool table. The cue ball is projected at the eight-ball with a speed of **7.85 m/s**. This velocity is at an angle of **30.0°** with respect to the y-axis. Both the cue ball and the eight-ball have an identical mass of **0.170 kg**. Following an elastic collision, the eight-ball moves in the negative x-direction, entering the side pocket. 

**Objective:**

Determine the velocity of the cue ball post-collision. Provide your answer in vector form.

**Diagram Explanation:**

- The pool table is illustrated with a coordinate system (x and y axes).
- The cue ball's direction of movement forms a **30° angle** from the y-axis, depicted with an arrow labeled with this angle.
- The eight-ball is stationary before the collision and is positioned in the path of the cue ball.
- The side pocket is located along the negative x-axis, where the eight-ball is directed post-collision.

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This scenario provides an excellent opportunity to apply the principles of conservation of momentum and energy, common in physics problems involving elastic collisions.
Transcribed Image Text:The image depicts a pool table scenario involving a collision between a cue ball and an eight-ball. Here's the content as it might appear on an educational website: --- ### Physics Problem: Elastic Collision on a Pool Table **Problem Description:** In the diagram shown, a cue ball is directed towards the eight-ball on a pool table. The cue ball is projected at the eight-ball with a speed of **7.85 m/s**. This velocity is at an angle of **30.0°** with respect to the y-axis. Both the cue ball and the eight-ball have an identical mass of **0.170 kg**. Following an elastic collision, the eight-ball moves in the negative x-direction, entering the side pocket. **Objective:** Determine the velocity of the cue ball post-collision. Provide your answer in vector form. **Diagram Explanation:** - The pool table is illustrated with a coordinate system (x and y axes). - The cue ball's direction of movement forms a **30° angle** from the y-axis, depicted with an arrow labeled with this angle. - The eight-ball is stationary before the collision and is positioned in the path of the cue ball. - The side pocket is located along the negative x-axis, where the eight-ball is directed post-collision. --- This scenario provides an excellent opportunity to apply the principles of conservation of momentum and energy, common in physics problems involving elastic collisions.
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