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
To solve this problem, we need to use the principle of moments. When mass is removed, the total moment of the aircraft changes, which in turn shifts the center of gravity (CG). Step 1: Determine the target center of gravity (CG) position. The CG limits are between 18 m and 22 m. The middle of these limits is: CG_target = 18 m + 22 m2 = 40 m2 = 20 m Step 2: Set up the moment equation. The initial moment of the aircraft is M_initial × CG_initial. When a mass m is removed from position X_removed, the new total mass is M_initial - m, and the new CG is CG_target. The moment equation is: (M_initial - m) × CG_target = (M_initial × CG_initial) - (m × X_removed) Given values: M_initial = 112000 kg CG_initial = 22.62 m CG_target = 20 m X_removed = 30 m Step 3: Substitute the values into the equation. (112000 kg - m) × 20 m = (112000 kg × 22.62 m) - (m × 30 m) Step 4: Expand and simplify the equation. (112000 × 20) - (20m) = (112000 × 22.62) - (30m) 2240000 - 20m = 2533440 - 30m Step 5: Isolate the term with m. Add 30m to both sides: 2240000 + 10m = 2533440 Subtract 2240000 from both sides: 10m = 2533440 - 2240000 10m = 293440 Step 6: Solve for m. m = (293440)/(10) m = 29344 kg The mass that must be removed is 29 344 kg. Comparing this to the given options: A) 8 680 kg. B) 43 120 kg. C) 16 529 kg. D) 29 344 kg. The correct option is D. The mass that must be removed is: D) 29 344 kg. That's 2 down. 3 left today — send the next one.