Impulse-momentum theorem

Steps:

• Convert mass to kilograms and note rebound direction: m = 0.055 kg, initial velocity = +30 m/s, final velocity = -20 m/s, so Δv = 50 m/s.
• Compute change in momentum magnitude: Δp = m × Δv = 0.055 kg × 50 m/s = 2.75 kg·m/s.
• Note contact time: Δt = 5.0 × 10^{-3} s = 0.005 s.
• Calculate average force on wall: F = Δp / Δt = 2.75 / 0.005 = 550 N.

Why D is correct:

• The impulse-momentum theorem states that average force equals change in momentum divided by time, yielding 550 N exactly.

Why the others are wrong:

• A: Uses Δv = 22 m/s (30 - 8 or similar miscalculation) with adjusted mass.
• B: Assumes full speed reversal to 30 m/s rebound, giving Δv = 60 m/s but halved force.
• C: Applies Δv = 30 m/s (ignores rebound speed) with double mass error.

Final answer: D