Final answer:
To calculate the maximum number of people that can be on the raft without the top of the raft sinking below the surface of the water, we need to consider the buoyant force acting on the raft. The buoyant force is equal to the weight of the water displaced by the raft. By comparing the weight of the water displaced by the raft to the weight of the raft and the people, we can determine the maximum number of people.
Step-by-step explanation:
To calculate the maximum number of people that can be on the raft without the top of the raft sinking below the surface of the water, we need to consider the buoyant force acting on the raft. The buoyant force is equal to the weight of the water displaced by the raft. If the average mass of a person is 75 kg, we can determine the maximum number of people by comparing the weight of the water displaced by the raft to the weight of the raft and the people.
The buoyant force can be calculated using Archimedes' Principle: Buoyant Force = Weight of Water Displaced = Density of Water x Volume of Water Displaced x Acceleration due to Gravity. Since the raft is floating, the weight of the water displaced by the raft is equal to the combined weight of the raft and the people on it.
Let's assume the density of water is about 1000 kg/m³. The volume of water displaced is the volume of the raft, which can be calculated by dividing the weight of the raft and the people by the density of water and acceleration due to gravity. So, the maximum number of people that can be on the raft without sinking can be found by dividing the weight of the raft and people by the average mass of a person.