A wooden raft has 85% of its volume submerged when it is floating down a river with a density of water being 9.90x10^2 kg/m^3. What is the density of the wooden raft?

To solve this problem, we need to apply the concept of buoyancy. The buoyant force acting on an object submerged in a fluid is equal to the weight of the fluid displaced by the object.

Let's assume the density of the wooden raft is represented by the symbol ρ_raft and its volume is given by V_raft.

We know that the buoyant force acting on the raft is equal to its weight, which is given by:

F_buoyant = ρ_water * V_raft * g

where ρ_water is the density of water, V_raft is the volume of the raft, and g is the acceleration due to gravity (approximately 9.81 m/s^2).

We also know that the volume of the raft that is submerged is 85%. Therefore, the volume of the raft that is above the water is given by:

V_above_water = (1 - 0.85) * V_raft
= 0.15 * V_raft

Since the total volume of the raft is equal to the sum of the volume above water and the volume submerged, we have:

V_raft = V_above_water + V_submerged

Since 85% of the volume is submerged, we have:

V_submerged = 0.85 * V_raft

Substituting this into our previous equation, we get:

V_raft = 0.15 * V_raft + 0.85 * V_raft
V_raft = V_raft

This means that the volume of the raft is self-consistent; it doesn't depend on any other factors. Therefore, we cannot determine the density of the raft based on the given information.

In order to calculate the density of the raft, we would need additional information such as the weight or mass of the raft.