This physics problem tests your understanding of fundamental physical laws and their applications. The step-by-step solution below breaks down the problem using relevant equations and physical reasoning.
ScanSolve AI Answer
Hey MET, good to see you again. To calculate the escape velocity, we use the formula: v_e = sqrt(2gR) where: • v_e is the escape velocity • g is the acceleration due to gravity on the Earth's surface (9.8 m/s^2) • R is the radius of the Earth (6.4 × 10^6 m) Step 1: Substitute the given values into the formula. v_e = sqrt(2 × 9.8 m/s)^2 × 6.4 × 10^6 m Step 2: Perform the multiplication inside the square root. v_e = sqrt(19.6 m/s)^2 × 6.4 × 10^6 m v_e = sqrt(125.44 × 10^6 m)^2/s^2 Step 3: Calculate the square root. v_e = sqrt(125.44) × sqrt(10^6) m/s v_e ≈ 11.20 × 10^3 m/s v_e ≈ 11200 m/s Step 4: Convert the velocity from meters per second (m/s) to kilometers per second (km/s). v_e = 11200 m/s × 1 km1000 m v_e ≈ 11.2 km/s Comparing this value to the given options: A. 25.3 km/s B. 4.2 km/s C. 4.0 km/s D. 11.3 km/s The calculated escape velocity of 11.2 km/s is closest to option D. The final answer is D. 11.3 km/s. Send me the next one 📸