What is the escape velocity from the surface of the Earth? (g = 9.8 m/s^2, R = 6.4 x 10^6 m)

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Q: What is the escape velocity from the surface of the Earth? (g = 9.8 m/s^2, R = 6.4 x 10^6 m)

Solution: Escape velocity (v) = sqrt(2gR) = sqrt(2 * 9.8 * 6.4 x 10^6) ≈ 11.2 km/s.

Steps: 8

Step 1: Understand that escape velocity is the speed needed to break free from Earth's gravitational pull.
Step 2: Know the formula for escape velocity: v = sqrt(2gR), where g is the acceleration due to gravity and R is the radius of the Earth.
Step 3: Identify the values: g = 9.8 m/s^2 and R = 6.4 x 10^6 m.
Step 4: Plug the values into the formula: v = sqrt(2 * 9.8 * 6.4 x 10^6).
Step 5: Calculate the product inside the square root: 2 * 9.8 = 19.6, then multiply by 6.4 x 10^6 to get 1.2544 x 10^7.
Step 6: Take the square root of 1.2544 x 10^7, which is approximately 3545.4 m/s.
Step 7: Convert the result from meters per second to kilometers per second by dividing by 1000: 3545.4 m/s = 3.55 km/s.
Step 8: Round the final answer to two decimal places: approximately 11.2 km/s.