A pirate is going to escape a ship by pretending to die and escape in a coffin.

Question

A pirate is going to escape a ship by pretending to die and escape in a coffin. The coffin has a cross-sectional area A and mass M. Empty, the coffin floats with its waterline at a height h1=10 cm above its bottom. When the pirate lies in the coffin with his cutlass and paddle (total mass m=90 kg) the waterline rises to a height h2=11 cm. What is the empty mass M of the coffin? What is the area A of the coffin? By setting M=A(0.10 m)(density of water) and M+90=A(0.11 m)(density of water), I got M=900 kg and A=9 m squared. This doesn't make a lot of sense, what am I doing wrong?

Explanation / Answer

vol of empty coffin in water = 10A vol of water displaced by coffin with pirate = 11A M=A(0.10 m)(density of water) and M+90=A(0.11 m)(density of water) A(0.10 m)(density of water)+90=A(0.11 m)(density of water) 100A + 90 = 110A A = 9 m^2 and M = 900 kg

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