In a one-dimensional elastic collision, a 2 kg object moving at 3 m/s hits a 1 kg object at rest. What is the final speed of the second object?

In a one-dimensional elastic collision, a 2 kg object moving at 3 m/s hits a 1 kg object at rest. What is the final speed of the second object?

• A. 2 m/s
• B. 3 m/s
• C. 4 m/s
• D. 5 m/s

Answer: (C)

In a one-dimensional elastic collision, both momentum and kinetic energy are conserved, and the relative speed of approach equals the relative speed of separation. Let the second object’s final speed be v2 and the first’s be v1. The momentum conservation gives 2×3 + 1×0 = 2v1 + v2, so 6 = 2v1 + v2. The elastic-collision relation for one dimension says v2 − v1 = u1 − u2 = 3, so v1 = v2 − 3. Substituting into the momentum equation: 6 = 2(v2 − 3) + v2 = 3v2 − 6, which yields v2 = 4 m/s. Therefore, the second object ends up moving at 4 m/s.

In a one-dimensional elastic collision, both momentum and kinetic energy are conserved, and the relative speed of approach equals the relative speed of separation. Let the second object’s final speed be v2 and the first’s be v1. The momentum conservation gives 2×3 + 1×0 = 2v1 + v2, so 6 = 2v1 + v2. The elastic-collision relation for one dimension says v2 − v1 = u1 − u2 = 3, so v1 = v2 − 3. Substituting into the momentum equation: 6 = 2(v2 − 3) + v2 = 3v2 − 6, which yields v2 = 4 m/s. Therefore, the second object ends up moving at 4 m/s.