https://file.aiquickdraw.com/mathbot/file/1737582461741k9w1rj29.jpg

The image you've provided involves an elastic collision between two masses, with the goal of determining the final velocity of mass 1 after the collision.

The formula given is:

\[
v_1f = \left( \frac{m_1 - m_2}{m_1 + m_2} \right) v_1i + \left( \frac{2m_2}{m_1 + m_2} \right) v_2i
\]

Where:
- \(m_1 = 0.311 \, \text{kg}\) (mass 1),
- \(m_2 = 0.0570 \, \text{kg}\) (mass 2),
- \(v_1i = +30.3 \, \text{m/s}\) (initial velocity of mass 1),
- \(v_2i = -19.2 \, \text{m/s}\) (initial velocity of mass 2).

### Step 1: Substituting values into the equation:

\[
v_1f = \left( \frac{0.311 - 0.0570}{0.311 + 0.0570} \right) \times 30.3 + \left( \frac{2 \times 0.0570}{0.311 + 0.0570} \right) \times (-19.2)
\]

### Step 2: Perform the calculation.

Let me compute this value for you. Given values
m1 = 0.311  # kg
m2 = 0.0570  # kg
v1i = 30.3  # m/s
v2i = -19.2  # m/s

# Calculate final velocity of mass 1 using the given formula
v1f = ((m1 - m2) / (m1 + m2)) * v1i + ((2 * m2) / (m1 + m2)) * v2i
v1fThe final velocity of mass 1 after the elastic collision is approximately \( 14.97 \, \text{m/s} \).

Would you like any further details or clarifications?

Here are 5 related questions:
1. How do you calculate the final velocity of mass 2 in an elastic collision?
2. What is the principle of conservation of momentum, and how does it relate to elastic collisions?
3. How do mass and velocity affect the outcome of an elastic collision?
4. What are some real-world examples of elastic collisions?
5. How does energy conservation apply in elastic collisions?

**Tip**: When solving problems with elastic collisions, always ensure that both momentum and kinetic energy are conserved!

Mass 1 (0.311 kg) is moving at +30.3 m/s. Mass 2 (0.0570 kg) is moving at -19.2 m/s. After an elastic collision of the two masses, what would the velocity of the mass 1 be?

This problem covers an elastic collision between two masses, where the initial velocities and masses are provided. The solution involves applying the conservation of momentum and using a specific formula to determine the final velocity of mass 1. Suitable for students in Grades 10-12 studying physics.

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