How far below the surface of the water is the boat's bottom when it is floating in water?

Question

A boat (with a flat bottom) and its cargo weigh 6,600 N. The area of the boat's bottom is 9 m². How far below the surface of the water is the boat's bottom when it is floating in water?

Answer 1

To determine how far below the surface of the water the boat's bottom is when it is floating in water, we can use Archimedes' principle, which states that the buoyant force on an object immersed in a fluid is equal to the weight of the fluid displaced by the object.

The buoyant force (B) acting on the boat is equal to the weight of the water it displaces. Let's assume that the boat is floating in freshwater, which has a density of 1000 kg/m^3. The weight of the water displaced is equal to the density of water times the volume of water displaced, which is equal to the area of the bottom of the boat times the depth of the boat's draft (d):

B = ρwater * V * g = ρwater * A * d * g

where ρwater is the density of water, V is the volume of water displaced, A is the area of the boat's bottom, d is the depth of the boat's draft, and g is the acceleration due to gravity.

The weight of the boat and its cargo is given as 6,600 N. This weight is balanced by the buoyant force, so we have:

B = 6,600 N

Substituting the values into the equation for the buoyant force, we get:

ρwater * A * d * g = 6,600 N

Solving for d, we get:

d = 6,600 N / (ρwater * A * g)

Substituting the values of ρwater, A, and g, we get:

d = 6,600 N / (1000 kg/m^3 * 9 m^2 * 9.81 m/s^2)

Simplifying the expression, we get:

d = 0.75 m

Therefore, the boat's bottom is 0.75 meters or 75 centimeters below the surface of the water when it is floating in water.