A 2 kg object moving at 5 m/s to the right collides elastically with a 3 kg object moving at 2 m/s to the left. What is the velocity of the 2 kg object after the collision?

Core Concept

For elastic collisions, both momentum and kinetic energy are conserved. Using conservation of momentum: m1v1i + m2v2i = m1v1f + m2v2f. (2)(5) + (3)(-2) = (2)v1f + (3)v2f. 10 - 6 = 2v1f + 3v2f. 4 = 2v1f + 3v2f. Using conservation of kinetic energy: (1/2)m1v1i² + (1/2)m2v2i² = (1/2)m1v1f² + (1/2)m2v2f². (1/2)(2)(25) + (1/2)(3)(4) = (1/2)(2)v1f² + (1/2)(3)v2f². 25 + 6 = v1f² + 1.5v2f². 31 = v1f² + 1.5v2f². Solving these simultaneously gives v1f = -0.4 m/s (to the left) and v2f = 2.8 m/s (to the right).