Perfectly elastic, head-on impact: equal masses Two balls of equal mass and perfectly elastic material lie on a smooth floor. One ball moving with speed v strikes the other, initially at rest. Choose the correct value among the options to represent the non-zero speed after impact.

Given dataEqual masses, perfectly elastic, one-dimensional impact; ball 1 speed initially = v, ball 2 initially at rest.

Concept/ApproachFor a perfectly elastic, head-on collision of equal masses, the velocities are exchanged.

Step-by-step calculationConservation of momentum: m·v + m·0 = m·v_1′ + m·v_2′ ⇒ v = v_1′ + v_2′Coefficient of restitution e = 1: v_2′ − v_1′ = vSolving the two linear equations ⇒ v_1′ = 0 and v_2′ = v.

InterpretationThe non-zero speed after impact equals v (the struck ball moves with v; the striker comes to rest).

Common pitfallsAssuming both move with the same speed after impact violates energy conservation for elastic collisions.

Final Answerv