A body of mass m undergoes an elastic collision with another identical body initially at rest. If the collision is not head-on, at what angle do the bodies travel relative to each other after the collision?

Step-by-step solution

Let the initial velocity of the first body be u and the second body be at rest. Let their final velocities be v ₁ and v ₂ . By conservation of linear momentum: m u = m v ₁ + m v ₂ u = v ₁ + v ₂ Taking the dot product of this equation with itself: u^2 = v₁^2 + v₂^2 + 2 v ₁ v ₂ Since the collision is elastic, kinetic energy is conserved: 1 2 mu^2 = 1 2 mv₁^2 + 1 2 mv₂^2 u^2 = v₁^2 + v₂^2 Comparing the two equations for u^2 : v₁^2 + v₂^2 = v₁^2 + v₂^2 + 2 v ₁ v ₂ 2 v ₁ v ₂ = 0 v ₁ v ₂ = 0 Since the collision is not he