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 = $\frac{m_1*u_1 + m_2*u_2}{(m_1+m_2)}$. Fraction of KE lost = $\frac{M}{m+M}$ when one body is at rest.

Partially Inelastic: 0 < e < 1. Use both momentum conservation and e = $\frac{v_2-v_1}{(u_1-u_2)}$ to solve.

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

Bouncing ball: e = sqrt$\frac{h_after}{h_before}$. Height after n bounces = $e^{2n}$ * $h_0$.

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