Final answer:
A boat with a mass of 4000 kg will displace 4 cubic meters of water, using the principle that the buoyant force is equal to the weight of the water the object displaces and the density of water being 1,000 kg/m³.
Step-by-step explanation:
To calculate how much water a boat would displace if the boat had a mass of 4000 kg, we can use the principle of buoyancy, also known as Archimedes' principle. According to this principle, the buoyant force on an object submerged in a fluid is equal to the weight of the fluid that the object displaces.
First, we need to consider the density of water, which is 1,000 kg/m³. Since the boat has a mass of 4000 kg, and assuming the boat is floating and not submerged, it will displace a volume of water with a mass equal to its own mass to stay afloat. Thus, the volume of water displaced would be equal to the mass of the boat divided by the density of water:
Volume = Mass / Density
Vw = 4000 kg / 1000 kg/m³ = 4 m³
Therefore, a boat with a mass of 4000 kg will displace 4 cubic meters of water.