Change in momentum as vector difference

Steps:

• Define positive direction as towards the bat: initial velocity = +20 m/s.
• Initial momentum = mass × initial velocity = 0.1 kg × 20 m/s = +2 kg m/s.
• Rebound velocity = -15 m/s (opposite direction).
• Final momentum = 0.1 kg × (-15 m/s) = -1.5 kg m/s.
• Change in momentum = final - initial = -1.5 - 2 = -3.5 kg m/s (magnitude 3.5 Ns).

Why D is correct:

• Matches the magnitude of Δp = m(v_f - v_i), where directions reverse, per momentum definition as mv.

Why the others are wrong:

• A: Ignores direction reversal, calculates only speed difference times mass (0.1 × 5 = 0.5, but wrong sign handling).
• B: Equals initial momentum alone (0.1 × 20 / 4, misapplied).
• C: Equals final momentum magnitude (0.1 × 15), not the change.

Final answer: D