What is the escape velocity from the surface of the Earth? (R = 6.4 × 10^6 m, g

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Question: What is the escape velocity from the surface of the Earth? (R = 6.4 × 10^6 m, g = 9.8 m/s²)

Options:

Correct Answer: 11.2 km/s

Solution:

Escape velocity v = √(2gR) = √(2 * 9.8 * 6.4 × 10^6) ≈ 11.2 km/s.

What is the escape velocity from the surface of the Earth? (R = 6.4 × 10^6 m, g = 9.8 m/s²)

What is the escape velocity from the surface of the Earth? (R = 6.4 × 10^6 m, g = 9.8 m/s²)

Step 1: Understand that escape velocity is the speed needed to break free from Earth's gravitational pull without any additional propulsion.
Step 2: Identify the formula for escape velocity, which is v = √(2gR), where g is the acceleration due to gravity and R is the radius of the Earth.
Step 3: Substitute the values into the formula. Here, g = 9.8 m/s² and R = 6.4 × 10^6 m.
Step 4: Calculate 2gR. First, multiply 2 by g: 2 * 9.8 = 19.6. Then multiply this by R: 19.6 * 6.4 × 10^6.
Step 5: Perform the multiplication: 19.6 * 6.4 = 125.44, so 125.44 * 10^6 = 1.2544 × 10^8.
Step 6: Take the square root of the result: v = √(1.2544 × 10^8).
Step 7: Calculate the square root, which is approximately 11,200 m/s or 11.2 km/s.

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