Final answer:
The man's average density is found by using Archimedes' principle to determine his total volume based on the volume of water displaced. Calculations show his volume as 0.0619 m³ and, consequently, his average density as approximately 970 kg/m³, which is option (b) 9.7 x 10² kg/m³.
Step-by-step explanation:
To calculate the average density of the man floating in freshwater, we need to use the principle of buoyancy, which is based on Archimedes' principle. According to this principle, the buoyant force acting on a submerged object is equal to the weight of the fluid displaced by the object. In this case, when the man is floating, the weight of the water displaced is equal to his weight because he is in equilibrium.
Since 97.0% of the man's volume is submerged, he displaces an amount of water with a volume equal to 97.0% of his volume. To find his density, we divide his mass by his total volume.
First, we calculate the volume of water displaced, which is also equal to 97.0% of the man's volume:
Vwater = (Weight of man) / (Density of freshwater)
Vwater = (60.0 kg) / (1000 kg/m³) = 0.0600 m³
Then, because only 97% is submerged, the total volume (Vman) is:
Vman = Vwater / 0.97
Vman = 0.0600 m³ / 0.97 ≈ 0.0619 m³
The average density (ρ) of the man is then:
ρ = Mass / Volume
ρ = 60.0 kg / 0.0619 m³ ≈ 970 kg/m³
When considering the options given, the answer closest to the calculated average density is 9.7 x 10² kg/m³. Therefore, the correct option is (b) 9.7 x 10² kg/m³.