The formulas to calculate the final velocities after an elastic collision are:
\[ m_1 \cdot v_{i1} + m_2 \cdot v_{i2} = m_1 \cdot v_{f1} + m_2 \cdot v_{f2} \]
\[ v_{f1} = \frac{(m_1 - m_2) \cdot v_{i1} + 2 m_2 \cdot v_{i2}}{m_1 + m_2} \]
\[ v_{f2} = \frac{2 m_1 \cdot v_{i1} - (m_1 - m_2) \cdot v_{i2}}{m_1 + m_2} \]
Where:
An elastic collision is the collision of two or more objects which act perfectly elastic, and as a result, momentum and energy are both conserved.
Let's assume the following values:
Using the formulas to calculate the final velocities:
\[ v_{f1} = \frac{(2 - 1) \cdot 3 + 2 \cdot (-1)}{2 + 1} = \frac{3 - 2}{3} = \frac{1}{3} \approx 0.33 \text{ m/s} \]
\[ v_{f2} = \frac{2 \cdot 2 \cdot 3 - (2 - 1) \cdot (-1)}{2 + 1} = \frac{12 + 1}{3} = \frac{13}{3} \approx 4.33 \text{ m/s} \]
The final velocities are approximately 0.33 m/s for Object 1 and 4.33 m/s for Object 2.
