Final answer:
A twin-sized air mattress with dimensions of 100 cm by 200 cm by 15 cm can support a person weighing up to 298 kg in freshwater, taking into account its own weight of 2 kg and the displacement of water.
Step-by-step explanation:
The question is about determining how heavy a person the twin-sized air mattress can hold when placed in freshwater. The volume of the air mattress is calculated by multiplying its dimensions: length (200 cm), width (100 cm), and height (15 cm).
Using the formula for the volume of a rectangular prism (Volume = length × width × height), we get 200 cm × 100 cm × 15 cm = 300,000 cubic centimeters (cm3).
Freshwater has a density of approximately 1 gram per cubic centimeter (g/cm3). Therefore, the air mattress can displace 300,000 grams (or 300 kilograms) of water.
Since the weight of the air mattress itself is 2 kg, the buoyant force provided by the water will be able to support an additional weight of up to 298 kilograms. Therefore, the air mattress could support a person weighing up to 298 kg under ideal conditions.