David builds a wood raft that weighs 100lbs (445 N). The bottom area of the raft is 4 meters and by 3 meters and the raft is 0.6 meters thick. When the raft is floats in water, what must the height of the water line be on the raft?

Buoyant force=Weight

ρ•V₁•g = Weight
V₁=x•y•z₁
ρ•x•y•z₁•g = Weight
z₁=Weight/ ρ•x•y•g =
=445/1000•4•3•9.8=0.0038 m =3.8 mm

To determine the height of the water line on the raft, we need to consider the principle of buoyancy. According to Archimedes' principle, the buoyant force acting on an object submerged in a fluid is equal to the weight of the fluid displaced by the object.

In this case, the weight of the raft is 100 lbs (445 N), which is the same as the buoyant force acting on it in water. We can use this information to calculate the volume of water displaced by the raft.

The formula to calculate the volume of a rectangular prism (which is equivalent to the volume of water displaced) is:
Volume = length × width × height

Given:
Length = 4 meters
Width = 3 meters
Thickness = 0.6 meters

Let's calculate the volume of water displaced by the raft:
Volume = 4 meters × 3 meters × height

Now, we can set up an equation to relate the weight of the raft to the volume of water displaced:
Weight of raft = Weight of displaced water
100 lbs (445 N) = Density of water × Volume of water

Density of water is approximately 1000 kg/m^3.

Substituting the values into the equation:
100 lbs (445 N) = 1000 kg/m^3 × (4 meters × 3 meters × height)

Simplifying the equation:
445 N = 1000 kg/m^3 × (12 meters × height)
445 N = 12000 kg/m^3 × height

Now we can solve for the height:
height = 445 N / (12000 kg/m^3)
height ≈ 0.037 meters

Therefore, the height of the water line on the raft is approximately 0.037 meters.