A 0.311 kg tennis racket moves east at $$ 30.3 \mathrm{~m} / \mathrm{s} $$. A 0.0570 kg ball moves east at $$ 19.2 \mathrm{~m} / \mathrm{s} $$. If the racket and the ball have an elastic collision, what would the velocity of the ball be afterwards? $$ v_{2 f}=[?] \mathrm{m} / \mathrm{s} $$ Remember East is positive ( + ): west is negative $$ (-) $$.

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To determine the final velocity of the ball ($$ v_{2f} $$) after an elastic collision with the tennis racket, we'll use the principles of conservation of momentum and kinetic energy.

### Given:
- **Mass of the racket ($$ m_1 $$)**: 0.311 kg
- **Initial velocity of the racket ($$ v_{1i} $$)**: 30.3 m/s east
- **Mass of the ball ($$ m_2 $$)**: 0.0570 kg
- **Initial velocity of the ball ($$ v_{2i} $$)**: 19.2 m/s east

### Elastic Collision Formulas:
For two objects undergoing a one-dimensional elastic collision, the final velocities are given by:

$$
v_{1f} = \left( \frac{m_1 - m_2}{m_1 + m_2} \right) v_{1i} + \left( \frac{2m_2}{m_1 + m_2} \right) v_{2i}
$$

$$
v_{2f} = \left( \frac{2m_1}{m_1 + m_2} \right) v_{1i} + \left( \frac{m_2 - m_1}{m_1 + m_2} \right) v_{2i}
$$

Alternatively, a simplified formula for $$ v_{2f} $$ is:

$$
v_{2f} = v_{2i} + \left( \frac{2m_1}{m_1 + m_2} \right) (v_{1i} - v_{2i})
$$

### Calculations:

1. **Sum of Masses**:
   $$
   m_1 + m_2 = 0.311 \, \text{kg} + 0.0570 \, \text{kg} = 0.368 \, \text{kg}
   $$

2. **Coefficient for $$ v_{1i} $$**:
   $$
   \frac{2m_1}{m_1 + m_2} = \frac{2 \times 0.311}{0.368} \approx 1.689
   $$

3. **Change in Velocity Due to Collision**:
   $$
   v_{2f} = 19.2 \, \text{m/s} + 1.689 \times (30.3 \, \text{m/s} - 19.2 \, \text{m/s}) 
   $$
   $$
   v_{2f} = 19.2 \, \text{m/s} + 1.689 \times 11.1 \, \text{m/s} 
   $$
   $$
   v_{2f} \approx 19.2 \, \text{m/s} + 18.78 \, \text{m/s} = 37.98 \, \text{m/s}
   $$

### Final Answer:
After rounding to an appropriate number of significant figures, the final velocity of the ball is:

$$
v_{2f} \approx 38.0 \, \text{m/s east}
$$

**Answer:** After the collision, the ball moves east with velocity approximately 38.0 m s⁻¹.
After the collision, the ball moves east at approximately 38.0 m/s.

A 0.311 kg tennis racket moves east at .
A 0.0570 kg ball moves east at .
If the racket and the ball have an elastic
collision, what would the velocity of
the ball be afterwards?

Remember East is positive ( + ): west is negative .

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A 0.311 kg tennis racket moves east at . A 0.0570 kg ball moves east at . If the racket and the ball have an elastic collision, what would the velocity of the ball be afterwards? Remember East is positive ( + ): west is negative .