What is the escape velocity from the surface of the Earth? (g = 9.8 m/s², R = 6.
Practice Questions
Q1
What is the escape velocity from the surface of the Earth? (g = 9.8 m/s², R = 6.4 × 10^6 m)
11.2 km/s
9.8 km/s
7.9 km/s
15 km/s
Questions & Step-by-Step Solutions
What is the escape velocity from the surface of the Earth? (g = 9.8 m/s², R = 6.4 × 10^6 m)
Step 1: Understand what escape velocity means. It is the speed needed to break free from the Earth's gravitational pull without any additional propulsion.
Step 2: Identify the formula for escape velocity, which is v = √(2gR). Here, 'g' is the acceleration due to gravity and 'R' is the radius of the Earth.
Step 3: Substitute the values into the formula. We know 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 result 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: Now take the square root of 1.2544 × 10^8 to find the escape velocity: √(1.2544 × 10^8).
Step 7: Calculate the square root. The square root of 1.2544 is approximately 11.2, and the square root of 10^8 is 10^4, which is 10,000.
Step 8: Combine the results: 11.2 * 10^4 m/s = 11.2 km/s.
