Final answer:
The mass of cargo and crew that the canoe can support without sinking is approximately 235 kg. The percentage of the canoe submerged with no cargo or crew cannot be identified without additional data on the canoe's density.
Step-by-step explanation:
The question concerns the mass of cargo and crew that a canoe can support on Iona Lake without sinking, which involves an application of Archimedes' Principle. A canoe with a volume of 250 L (which is 0.25 m³) and a mass of 15 kg will displace an equal volume of water. Since the density of water is 1000 kg/m³, the weight of the displaced water is (0.25 m³) × (1000 kg/m³) × (9.8 m/s²) = 2450 N. This is the maximum buoyant force that can act on the canoe. The weight of the canoe is 15 kg × 9.8 m/s² = 147 N. Hence, the additional weight of cargo and crew that the canoe can support is 2450 N - 147 N = 2303 N, which equals to 2303 N / 9.8 m/s² ≈ 235 kg.
To find what percentage of the canoe will be submerged if all of the cargo and crew are removed, we look at the weight of the canoe compared to the buoyant force when it is empty. With no cargo or crew, the canoe's weight will cause a buoyant force equal to its own weight to keep it afloat. This implies that the canoe when empty will not be fully submerged, and will displace water with weight equal to its own. With the canoe displace less water when empty, only a percentage of it will be submerged. However, since no precise density for the canoe is provided, the exact percentage cannot be determined without additional data.