What is the escape velocity from the surface of Earth (radius R = 6.37 10^6 m, mass M = 5.97 10^24 kg, G = 6.674 * 10^-11 N m^2/kg^2)?
Answer and explanation
Correct answer: A. 11.2 km/s
- Step 1: Escape velocity formula: v_{esc} = sqrt(2 G M / R).
- Step 2: Numerator: 2 (6.674 10^-11) (5.97 10^24) = 7.969 * 10^14.
- Step 3: Divide by R: 7.969 10^14 / (6.37 10^6) = 1.251 * 10^8.
- Step 4: Square root: sqrt(1.251 * 10^8) = 11185 m/s = 11.2 km/s.
Answer
11.2 km/s.
Why not the others: 7.9 km/s is orbital speed in low Earth orbit, sqrt(G*M/R); 22.4 km/s doubles the escape speed; 15.8 km/s multiplies orbital speed by 2 instead of sqrt(2).
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