Impulse-Momentum Theorem for Inelastic Collision

Steps:

• Calculate initial momentum: X contributes +4.0 kg m/s (right positive), Y contributes -1.0 kg m/s; total = +3.0 kg m/s.
• Find final velocity: total mass 3.0 kg, so v_f = 3.0 / 3.0 = +1.0 m/s.
• Determine change in momentum for X: Δp_X = 2.0 kg (1.0 - 2.0) m/s = -2.0 kg m/s.
• Compute average force: F_avg = Δp_X / Δt = -2.0 / 0.20 s = -10 N (magnitude 10 N).

Why B is correct:

• Matches F_avg = |Δp_X| / Δt from impulse theorem, where impulse equals change in momentum.

Why the others are wrong:

• A: Underestimates Δp_X magnitude (uses 0.66 kg m/s instead of 2.0).
• C: Assumes elastic collision or doubles Δp_X.
• D: Ignores Y's momentum, using only X's initial speed change.

Final answer: B