Before V₁₁ = 24m/s V₂;=0m/s a) How fast is each ball moving after the collision? After QJ Buecos 38" 46° Vaf Vif sily animonial to giens sall) Saoisillen sid teils selv lad dous live dgis wollt 5) Calculate the percent kinetic energy lost in the collision, AK/K₂ x 100%, to determine "how elastic" he collision was (perfectly elastic is 0% lost).

College Physics
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Chapter1: Units, Trigonometry. And Vectors
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**Problem Statement:**

In a game of billiards, to put the red ball into the corner pocket, it must be hit at a 38° angle away from the line connecting it to the cue ball. The cue ball hits it with a speed of 2.4 m/s, and the cue ball itself heads off at a 46° angle away from the corner pocket. The two balls have the same mass, and the shot is successful.

**Diagrams:**

- **Before Collision:**
  - The cue ball \( c \) is moving towards the red ball \( r \) with an initial velocity \( v_{1i} = 2.4 \, \text{m/s} \).
  - The red ball \( r \) is stationary with an initial velocity \( v_{2i} = 0 \, \text{m/s} \).

- **After Collision:**
  - The red ball moves at an angle of 38° with velocity \( v_{2f} \).
  - The cue ball moves at an angle of 46° with velocity \( v_{1f} \).

**Questions:**

a) How fast is each ball moving after the collision?

b) Calculate the percent kinetic energy lost in the collision, \(\Delta K / K_i \times 100\%\), to determine "how elastic" the collision was (perfectly elastic is 0% lost).

**Notes on Diagrams:**

- The "Before" section shows the path and velocity of the cue ball approaching the red ball. 
- The "After" section illustrates both balls deflecting away at their respective angles post-collision. 
- Both diagrams label angles and velocities as described.
Transcribed Image Text:**Problem Statement:** In a game of billiards, to put the red ball into the corner pocket, it must be hit at a 38° angle away from the line connecting it to the cue ball. The cue ball hits it with a speed of 2.4 m/s, and the cue ball itself heads off at a 46° angle away from the corner pocket. The two balls have the same mass, and the shot is successful. **Diagrams:** - **Before Collision:** - The cue ball \( c \) is moving towards the red ball \( r \) with an initial velocity \( v_{1i} = 2.4 \, \text{m/s} \). - The red ball \( r \) is stationary with an initial velocity \( v_{2i} = 0 \, \text{m/s} \). - **After Collision:** - The red ball moves at an angle of 38° with velocity \( v_{2f} \). - The cue ball moves at an angle of 46° with velocity \( v_{1f} \). **Questions:** a) How fast is each ball moving after the collision? b) Calculate the percent kinetic energy lost in the collision, \(\Delta K / K_i \times 100\%\), to determine "how elastic" the collision was (perfectly elastic is 0% lost). **Notes on Diagrams:** - The "Before" section shows the path and velocity of the cue ball approaching the red ball. - The "After" section illustrates both balls deflecting away at their respective angles post-collision. - Both diagrams label angles and velocities as described.
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