Free fall time ratio from inverse square root of gravity

Steps:

• Distance s = (1/2) g t² applies to both planets, with same s.
• Time t = sqrt(2s / g), so t ∝ 1/sqrt(g).
• Ratio Tm/Te = sqrt(g_E / g_M), where g_E = 9.8 m/s² and g_M = 3.7 m/s².
• sqrt(9.8 / 3.7) = sqrt(2.65) ≈ 1.63.

Why C is correct:

• 1.63 matches sqrt(g_E / g_M) from the kinematic equation for free fall under constant acceleration.

Why the others are wrong:

• A: Equals sqrt(g_M / g_E) ≈ 0.38, the inverse ratio.
• B: Equals sqrt(g_M / g_E) ≈ 0.615, another inverse approximation.
• D: Equals g_E / g_M ≈ 2.65, the direct acceleration ratio.

Final answer: C