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!