Momentum Reversal in Elastic Collision

Steps:

• Define initial momentum as $\vec{p_i} = mv$ (towards wall).
• For perfectly elastic collision, speed remains $v$, but direction reverses, so final momentum $\vec{p_f} = -mv$.
• Change in momentum $\Delta \vec{p} = \vec{p_f} - \vec{p_i} = -mv - mv = -2mv$.
• Magnitude of change is $2mv$.

Why D is correct:

• In elastic collisions with a stationary wall, momentum fully reverses, doubling the change from initial value per Newton's laws.

Why the others are wrong:

• A: Zero implies no velocity change, but rebound occurs.
• B: 0.5 mv has no basis; change isn't halved.
• C: mv equals initial momentum, ignoring reversal.

Final answer: D