How Deep Does a Ferry Sink with Added Weight?

[Falinox]

Homework Statement

A) A ferry boat has dimensions of 25 m by 10 m by 5 m and a mass of 50,000 kg. How far below the surface of the water will the bottom of the boat be? (ρ=1015 kg/m3)

B) If 12 cars of mass 1500 kg each drive onto the ferry, how much lower does the ferry sink into the water?

The Attempt at a Solution

The object is floating so I know the weight is equal to the buoyant force.

The buoyant force equals...
Fbuoy = PbotA-PtopA (Pressure at the bottom times Area - Pressure at the top times Area)
Fbuoy = ΔP(A)
Fbuoy = (pf)(g)(hA)
Fbuoy = pf(g)(V)

Need help getting started, am I on the right track? Where do I go from here? Thanks in advance.

 

[Undoubtedly0]

Greetings! For part A, Archimedes' principle states that the force of buoyancy on a submerged object is equal to the weight of the fluid displaced. Thus, when the boat is stationary, the boat's weight and the force of buoyancy are balanced: m_Bg = F_B, where F_B = m_Wg = ρVg. Since you know the boat's mass and the density of water, you can solve m_B = ρV for V, the volume of the boat that is submerged.