Work out elastic collision instantly with clear inputs, formula shown and shareable results.
A perfectly elastic collision conserves both momentum and kinetic energy, and solving the pair of equations gives the standard result for each final velocity. With 2 kg at 6 m/s meeting 3 kg at -2 m/s, the first rebounds at -3.6 m/s and the second moves off at 4.4 m/s. Momentum and energy totals are printed so you can confirm nothing was lost.
First body
v1 = ((m1 - m2)u1 + 2 m2 u2) / (m1 + m2)
Second body
v2 = ((m2 - m1)u2 + 2 m1 u1) / (m1 + m2)
They swap velocities exactly - the basis of the classic billiard-ball result and of Newton's cradle.
Only approximately. Hard steel balls and gas molecules come close; anything that makes a noise or deforms has lost energy.