Final answer:
The displacement of the aircraft carrier due to the landing of the fighter airplane is 28.3 cubic meters, calculated using Archimedes' principle, the known weight of the airplane, and the density of seawater.
Step-by-step explanation:
To calculate the displacement of the aircraft carrier as the 29,000-kg fighter airplane lands, we need to consider the principle of flotation which is based on Archimedes' principle. This principle states that the upward buoyant force that is exerted on a body immersed in a fluid, whether fully or partially submerged, is equal to the weight of the fluid that the body displaces.
Since the aircraft carrier sinks 0.20 cm deeper into the water when the airplane lands on it, this additional displacement of water must be equal to the weight of the airplane. The weight of the airplane is the mass of the airplane multiplied by the acceleration due to gravity (W = m*g). Here, the mass m is 29,000 kg, and g is approximately 9.81 m/s².
The weight of the airplane is:
W = m*g = 29,000 kg * 9.81 m/s² = 284,490 N
Since the weight of the displaced water equals the weight of the airplane, we can set them equal to each other:
Weight of displaced water = Weight of airplane
Density (ρ) of seawater is approximately 1025 kg/m³. The volume of displaced water (V) can be found using the formula:
V = mass of displaced water/ ρ
And since mass = weight/g, we have:
V = W/gρ = 284,490 N / (9.81 m/s² * 1025 kg/m³) = 28.3 m³
Therefore, the displacement of the aircraft carrier due to the landing of the fighter airplane is 28.3 cubic meters.