Final answer:
Boat manufacturers generally use an average weight of 150 pounds per person for capacity calculations, based on buoyancy. The buoyant force supporting the boat must exceed the combined weight of the boat and its load. This ensures safe navigation by adhering to the principle of buoyancy and properly designed hulls that minimize drag.
Step-by-step explanation:
Boat manufacturers typically use an average weight of about 150 pounds per person to calculate maximum capacity. This is related to the principle of buoyancy, where the maximum buoyant force produced by the displaced water must be greater than the weight of the boat including its passengers. Using an average weight per person helps to ensure that the boat does not exceed this capability. For example, if the boat can carry a load nine times its own weight without sinking, this ratio is important to avoid overloading it past the safety limits, like exceeding 3,500 pounds for 20 men on a water taxi, indicating a potential safety concern.
The buoyant force is the weight of the water volume the ship displaces. It's important for the design of the hull to ensure efficiency and safety, as factors like drag should be considered at low speeds (less than 1/600th of the weight of the ship). Thus, calculations of buoyant force and passenger weight contribute to the overall engineering and operational practices for watercraft navigation.
Measurements like the weight of a ship or boat, or the weight of its passengers, can be represented in different forms, such as decimal or scientific notation. For instance, the maximum takeoff weight of a plane may be given as a large number or in scientific notation for simplicity and ease of understanding.