Final answer:
When floating in freshwater with a density very close to 995 kg/m³, approximately 99.5% of a person's body will be submerged. However, in saltwater with a density of 1027 kg/m³, approximately 96.88% of a person's body will need to be submerged to float.
Step-by-step explanation:
To determine the fraction of a person that is submerged when floating gently, we can apply the principle of flotation based on Archimedes' Principle. According to this principle, the buoyant force on a submerged object is equal to the weight of the fluid displaced by the object. For an object floating in equilibrium, the buoyant force is also equal to the weight of the object.
Freshwater floating
In the case of freshwater, the density is typically around 1000 kg/m³. If a person's body has a density of 995 kg/m³, the fraction of the body that needs to be submerged to displace a volume of water equal to the weight of the body can be found using their relative densities. Since the person's density is 995 kg/m³ and freshwater is 1000 kg/m³, the fraction submerged (Φ) would be:
Φ = Density of person / Density of freshwater = 995 / 1000
Φ = 0.995
Therefore, about 99.5% of the person's volume would need to be submerged for them to float in freshwater.
Saltwater floating
For saltwater, with a density of 1027 kg/m³, the calculation is similar:
Φ = Density of person / Density of saltwater = 995 / 1027
Φ ≈ 0.9688
About 96.88% of the person's volume would need to be submerged for them to float in saltwater.