As shown in the figure, a billiard ball with mass m₂ is initially at rest on a horizontal, frictionless table. A second billiard ball with mass m, moving with a speed 2.00 m/s, collides with m₂. Assume m₁ moves initially along the +x-axis. After the collision, m₁ moves with speed 1.00 m/s at an angle of 8 = 53.0° to the positive x-axis. (Assume m₁ = 0.200 kg and m₂ = 0.300 kg.) a my = Before the collision Vi m2 b After the collision (a) Determine the speed (in m/s) of the 0.300 kg ball after the collision. m/s vyysin 0 Vaf sin o v cos 41 Vof Cos √2f (b) Find the fraction of kinetic energy transferred away or transformed to other forms of energy in the collision. |AK| K₁

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As shown in the figure, a billiard ball with mass \( m_2 \) is initially at rest on a horizontal, frictionless table. A second billiard ball with mass \( m_1 \) moving with a speed 2.00 m/s, collides with \( m_2 \). Assume \( m_1 \) moves initially along the +x-axis. After the collision, \( m_1 \) moves with speed 1.00 m/s at an angle of \( \theta = 53.0^\circ \) to the positive x-axis. (Assume \( m_1 = 0.200 \, \text{kg} \) and \( m_2 = 0.300 \, \text{kg} \).)

**Diagram Explanation:**

- *Before the collision*:
  - A blue ball labeled \( m_1 \) with an arrow labeled \( \vec{v}_{1i} \) indicating initial velocity moving rightward.
  - An orange ball labeled \( m_2 \) is at rest.

- *After the collision*:
  - The blue ball has a velocity \( \vec{v}_{1f} \) directed at angle \( \theta = 53.0^\circ \) from the x-axis with components \( v_{1f} \cos \theta \) (horizontal) and \( v_{1f} \sin \theta \) (vertical).
  - The orange ball \( m_2 \) has a velocity \( \vec{v}_{2f} \) with components \( v_{2f} \cos \phi \) (horizontal) and \( v_{2f} \sin \phi \) (vertical).

**Questions:**

(a) Determine the speed (in m/s) of the 0.300 kg ball after the collision.

\[\text{Answer:} \hspace{3cm} \, \text{m/s} \]

(b) Find the fraction of kinetic energy transferred away or transformed to other forms of energy in the collision.

\[\frac{|\Delta K|}{K_i} = \hspace{3cm} \]
Transcribed Image Text:As shown in the figure, a billiard ball with mass \( m_2 \) is initially at rest on a horizontal, frictionless table. A second billiard ball with mass \( m_1 \) moving with a speed 2.00 m/s, collides with \( m_2 \). Assume \( m_1 \) moves initially along the +x-axis. After the collision, \( m_1 \) moves with speed 1.00 m/s at an angle of \( \theta = 53.0^\circ \) to the positive x-axis. (Assume \( m_1 = 0.200 \, \text{kg} \) and \( m_2 = 0.300 \, \text{kg} \).) **Diagram Explanation:** - *Before the collision*: - A blue ball labeled \( m_1 \) with an arrow labeled \( \vec{v}_{1i} \) indicating initial velocity moving rightward. - An orange ball labeled \( m_2 \) is at rest. - *After the collision*: - The blue ball has a velocity \( \vec{v}_{1f} \) directed at angle \( \theta = 53.0^\circ \) from the x-axis with components \( v_{1f} \cos \theta \) (horizontal) and \( v_{1f} \sin \theta \) (vertical). - The orange ball \( m_2 \) has a velocity \( \vec{v}_{2f} \) with components \( v_{2f} \cos \phi \) (horizontal) and \( v_{2f} \sin \phi \) (vertical). **Questions:** (a) Determine the speed (in m/s) of the 0.300 kg ball after the collision. \[\text{Answer:} \hspace{3cm} \, \text{m/s} \] (b) Find the fraction of kinetic energy transferred away or transformed to other forms of energy in the collision. \[\frac{|\Delta K|}{K_i} = \hspace{3cm} \]
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