A 0.500 kg object moving at 4.00 m/s collides elastically with a stationary 3.50 kg object. Solving the momentum and kinetic energy equations gives two solutions for the first object's final velocity, one of which is discarded as trivial. What are the physically meaningful final velocities?

1. Solving the quadratic that comes from combining momentum and kinetic energy conservation gives two roots for the first object's final velocity, 4.00 m/s and -3.00 m/s. 2. The root of 4.00 m/s just reproduces the initial condition, so it is discarded as not describing an actual collision outcome. 3. The meaningful root is -3.00 m/s, meaning the small object bounces backward. 4. Using v2 prime equal to (m1 divided by m2) times (v1 minus v1 prime) with v1 prime of -3.00 m/s gives v2 prime of 1.00 m/s for the larger object. 5. This matches the intuitive picture of a small object bouncing off a much larger, initially stationary one, which barely moves forward afterward. _Source: OpenStax College Physics (CC BY 4.0), Ch 8 "Linear Momentum and Collisions", section 8.4 Elastic Collisions in One Dimension_