Understanding Conservation of Momentum
Conservation of momentum states that the total momentum of a closed system remains constant if no external forces act on it. This principle is essential for solving numerical problems in physics.

Key Concepts
- **Momentum (p)**: Defined as the product of mass (m) and velocity (v).
- Formula: \( p = m \times v \)
- **Closed System**: A system where no external forces influence the momentum of the objects involved.

Steps to Solve Numerical Problems
1. **Identify the System**
- Determine the objects in the problem and ensure that the system is closed.
2. **Define Initial and Final States**
- Establish the initial and final conditions of the system.
- For example, consider two colliding objects: Object A with mass \( m_A \) and velocity \( v_{A_i} \), and Object B with mass \( m_B \) and velocity \( v_{B_i} \).
3. **Apply Conservation of Momentum**
- Use the formula:
\[
m_A \cdot v_{A_i} + m_B \cdot v_{B_i} = m_A \cdot v_{A_f} + m_B \cdot v_{B_f}
\]
- Here, \( v_{A_f} \) and \( v_{B_f} \) are the final velocities after the interaction.
4. **Solve for Unknowns**
- Rearrange the equation to solve for the unknown variable(s), using algebraic techniques.
5. **Check Units and Reasonableness**
- Ensure that units are consistent and the final answer makes physical sense.

Example Problem
- **Given**: \( m_A = 2 \, \text{kg} \), \( v_{A_i} = 3 \, \text{m/s} \); \( m_B = 3 \, \text{kg} \), \( v_{B_i} = -2 \, \text{m/s} \)
- **Find**: Final velocities after collision, assuming a perfectly elastic collision.

Conclusion
Using these steps, you can systematically approach and solve problems involving the law of conservation of momentum. Always remember to check the physicality of your answers!

by understanding the questions and relating them through given formula