Free fall speed ratio using kinematics

Steps:

• Use v = √(2gh) for speed after free fall from rest.
• Earth: v_E = √(2 g_E × 2) = √(4 g_E) = 2 √g_E.
• Moon: g_M = 0.16 g_E, h_M = 4 m, so v_M = √(2 × 0.16 g_E × 4) = √(1.28 g_E).
• Ratio v_E / v_M = √(4 g_E / 1.28 g_E) = √(3.125) ≈ 1.77, which rounds to 1.8.

Why A is correct:

• Matches the kinematic formula v = √(2gh), yielding √(g_E h_E / g_M h_M) = √(3.125) ≈ 1.8 exactly.

Why the others are wrong:

• B: Assumes g_M ≈ 1/6 g_E without height adjustment, giving √(2 / (2/3)) ≈ 2.45.
• C: Overestimates by ignoring height doubling, like √(g_E / g_M) ≈ √6.25 ≈ 2.5, then inflating.
• D: No physical basis; perhaps confusing with time ratios or unrelated factors.

Final answer: A