Final answer:
The twin-sized air mattress with dimensions of 100 cm by 200 cm by 15 cm can support a person weighing up to 298 kg when placed in freshwater, using Archimedes' principle of buoyancy.
Step-by-step explanation:
The question at hand involves calculating the buoyant force exerted by freshwater on an air mattress to determine how heavy a person it could support. This is a physics problem that applies the principle of buoyancy, which is covered in high school physics courses.
Buoyancy is a force exerted by a fluid that opposes an object's weight. The buoyant force on an object submerged in a fluid is equal to the weight of the fluid displaced by the object. This principle is often referred to as Archimedes' principle.
In the case of the twin-sized air mattress, its volume is 100 cm x 200 cm x 15 cm, which equals 300,000 cubic centimeters. Freshwater has a density of approximately 1 gram per cubic centimeter. Therefore, the buoyant force is equivalent to the weight of 300,000 grams of water, or 300 kilograms.
Subtracting the weight of the mattress (2 kg) from the maximum buoyant force (300 kg), we understand that the air mattress can support a person weighing up to 298 kg without sinking.