Collisions are analyzed using conservation of momentum (always valid, no external forces during collision) and energy considerations.

Elastic: Both momentum and KE conserved. e = 1. Equal masses: complete velocity exchange. Heavy hits light: both continue forward. Light hits heavy: light bounces back.

Perfectly Inelastic: Momentum conserved, maximum KE loss. Bodies stick together: v = (m_1u_1 + m_2u_2)/(m_1+m_2). Fraction of KE lost = M/(m+M) when one body is at rest.

Partially Inelastic: 0 < e < 1. Use both momentum conservation and e = (v_2-v_1)/(u_1-u_2) to solve.

2D Elastic (equal masses, one at rest): Balls separate at 90 degrees.

Bouncing ball: e = sqrt(h_after/h_before). Height after n bounces = e^{2n} * h_0.

Strategy: Always use momentum conservation first, then energy/restitution for the second equation.