An 33-kg person puts on a life jacket, jumps into the water, and floats. The jac

Question

An 33-kg person puts on a life jacket, jumps into the water, and floats. The jacket has a volume of 2.9 times 10-2 m3 and is completely submerged under the water. The volume of the person's body that is under water is 5.8 times 10-2 m3. What is the density of the life jacket? An 33-kg person puts on a life jacket, jumps into the water, and floats. The jacket has a volume of 2.9 times 10-2 m3 and is completely submerged under the water. The volume of the person's body that is under water is 5.8 times 10-2 m3. What is the density of the life jacket?

Explanation / Answer

Let d = density of the life jacket (kg/m^3)
=> mass of the life jacket = 2.9 x 10^-2 d kg

As the person with the life jacket floats in water,
weight of the person + life jacket = weight of water displaced
=> (33 + 2.9 x 10^-2 d) g = (5.8 x 10^-2 + 2.9 x 10^-2) x 1000 g
=> 33 + 2.9 x 10^-2 d = 87
=> d = (87 - 33) / 2.29x 10^-2 kg/m^3
=> d = 0.235 x 10^3 kg/m^3.

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