Elastic Collision

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Two balls of equal mass undergo a head-on elastic collision. If one ball was initially at rest and the other had velocity v, what are their velocities after collision?

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1. **Key Characteristic**: In a head-on elastic collision between two objects of **identical mass**, the velocities are **exchanged**.
2. **Conservation Proof**:
   - Momentum: $mv + 0 = mv_1 + mv_2 \implies v = v_1 + v_2$.
   - Kinetic Energy: $\frac{1}{2}mv^2 = \frac{1}{2}mv_1^2 + \frac{1}{2}mv_2^2 \implies v^2 = v_1^2 + v_2^2$.
3. **Resulting State**: The only physical solution where speeds are real and positive is $v_1 = 0$ and $v_2 = v$.
4. **Conclusion**: The incoming ball stops completely, and the target ball launches with the original speed.

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Elastic Collision

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