Consider a head-on elastic collision between two bodies possessing identical masses. In this situation:

Step-by-step solution

Let the masses of the two bodies be m₁ = m₂ = m . Let their initial velocities be u₁ and u₂ , and final velocities be v₁ and v₂ . From the conservation of linear momentum: m u₁ + m u₂ = m v₁ + m v₂ u₁ + u₂ = v₁ + v₂ For a perfectly elastic head-on collision, the coefficient of restitution is e = 1 : v₂ - v₁ = u₁ - u₂ Adding the two equations yields 2v₂ = 2u₁ v₂ = u₁ . Subtracting the second equation from the first yields 2v₁ = 2u₂ v₁ = u₂ . Thus, the velocities of the two bodies are interchanged. Since the velociti