A puck with a mass m=0.15 kg has an initial speed of vpi=10.54 m/s at an angle of theta =30.9 degrees with respect to the x-axis. The puck hits a stick with a mass ms=0.24 kg  which is initially at rest as indicated in the figure. The puck leaves with a speed of vpf=4.09 m/s at an angle phi=40 degrees with respect to the y-axis. The collision occurs on ice, so friction can be neglected during the collision. How do I find the x and y components of the final velocity of the center of mass of the stick and the change in the translational kinetic energy of the Puck +Stick system?

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A puck with a mass m=0.15 kg has an initial speed of vpi=10.54 m/s at an angle of theta =30.9 degrees with respect to the x-axis. The puck hits a stick with a mass ms=0.24 kg  which is initially at rest as indicated in the figure. The puck leaves with a speed of vpf=4.09 m/s at an angle phi=40 degrees with respect to the y-axis. The collision occurs on ice, so friction can be neglected during the collision.

How do I find the x and y components of the final velocity of the center of mass of the stick and the change in the translational kinetic energy of the Puck +Stick system?

The image depicts a two-dimensional coordinate system with axes labeled \(x\) and \(y\). In the diagram, a vector is shown originating from the origin, represented by an arrow. This vector forms two angles with the x-axis.

- **Angle \(\theta\)**: This angle is formed between the vector and a line parallel to the x-axis, indicating the initial vector direction towards the circular path.
  
- **Angle \(\phi\)**: This angle is measured from the vertical line (aligned with the y-axis) to the vector. It represents the orientation of the vector concerning the y-axis.

The circular symbol at the base of the vector suggests a point of origin or pivot, from which the vector is projected. The thin vertical line, which the vector appears to rebound off, can indicate a surface or barrier, emphasizing the reflection or change in direction of the vector. The angles \(\theta\) and \(\phi\) are crucial for understanding the vector's initial and resulting direction.
Transcribed Image Text:The image depicts a two-dimensional coordinate system with axes labeled \(x\) and \(y\). In the diagram, a vector is shown originating from the origin, represented by an arrow. This vector forms two angles with the x-axis. - **Angle \(\theta\)**: This angle is formed between the vector and a line parallel to the x-axis, indicating the initial vector direction towards the circular path. - **Angle \(\phi\)**: This angle is measured from the vertical line (aligned with the y-axis) to the vector. It represents the orientation of the vector concerning the y-axis. The circular symbol at the base of the vector suggests a point of origin or pivot, from which the vector is projected. The thin vertical line, which the vector appears to rebound off, can indicate a surface or barrier, emphasizing the reflection or change in direction of the vector. The angles \(\theta\) and \(\phi\) are crucial for understanding the vector's initial and resulting direction.
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