Final answer:
The air mattress can hold up to 298 kilograms, taking into account the concept of buoyancy and the weight of the mattress itself, which is 2 kilograms.
Step-by-step explanation:
The question is asking how heavy a person the air mattress could hold if it is used in freshwater. To answer this, we need to understand the concept of buoyancy, which is a physics concept. Buoyancy determines whether an object will sink or float in a fluid, including gases and liquids like water.
For an object to float, the weight of the volume of water it displaces must be equal to or greater than the weight of the object. The air mattress dimensions are given as 100 cm by 200 cm by 15 cm which gives a volume of 300,000 cubic centimeters. Freshwater has a density of approximately 1 gram per cubic centimeter.
Thus, the weight of water displaced by the mattress is equivalent to its volume times the density of water, which equals 300,000 grams or 300 kilograms. When considering the weight of the mattress (2 kg), the air mattress could support a person weighing up to 298 kilograms in freshwater, assuming the weight is evenly distributed.