Final answer:
To calculate the number of people a boat can hold before sinking, one must compute the boat's volume, convert it to weight using the density of water, and then divide by the mass of one person. The 5.0 m wide, 5.0 m deep, and 10.0 m long boat can support approximately 3333 people each weighing 75 kg.
Step-by-step explanation:
The question revolves around the principles of buoyancy and Archimedes' principle, which states that the upward buoyant force exerted on a body immersed in a fluid is equal to the weight of the fluid that the body displaces. To determine how many people the boat can hold before it sinks, you need to calculate the volume of water the boat can displace without sinking, which is equivalent to its own volume submersed. Here's a step-by-step explanation:
- Calculate the volume of the boat: Volume = length × width × depth = 10.0 m × 5.0 m × 5.0 m = 250 m³.
- Determine the maximum weight the boat can support without sinking: Since the density of water is approximately 1000 kg/m³, the weight of the water displaced by the full volume of the boat is equal to the maximum weight the boat can support without sinking: Weight = Volume × density of water × gravity = 250 m³ × 1000 kg/m³ × 9.8 m/s² = 2450000 N.
- Convert the maximum weight supported to a mass: Mass = Weight / gravity = 2450000 N / 9.8 m/s² = 250000 kg.
- Calculate the number of people the boat can hold: Number of people = Mass of the boat's carrying capacity / mass of one person = 250000 kg / 75 kg = approximately 3333 people.
Therefore, the boat can hold about 3333 people each with a mass of 75 kg before it would be in danger of sinking.