Conservation of Momentum in Separation

Steps:

• The combined probe is initially at rest relative to the comet, so total momentum is zero.
• After separation, the lander moves toward the comet at 3.0 m/s; define toward the comet as negative direction.
• Let $v_o$ be the orbiter's speed away (positive); apply conservation: $170 v_o + 100(-3.0) = 0$.
• Solve: $170 v_o = 300$, so $v_o = 300 / 170 \approx 1.8$ m/s.

Why A is correct:

• Matches the calculated orbiter speed from momentum conservation, where velocities are inversely proportional to masses.

Why the others are wrong:

• B: Overestimates by assuming equal masses or velocities.
• C: Equals lander speed, ignoring mass difference in momentum balance.
• D: Adds speeds without considering direction or conservation law.

Final answer: A