A 70.3-kg person puts on a life jacket, jumps into the water, and floats. The jacket has a volume of 3.07 x 10-2 m3 and is completely submerged under the water. The volume of the person's body that is underwater is 6.49 x 10-2 m3. What is the density of the life jacket?

Answer 1

M = 70.3 kg = Mass of the person.
Dj = Density of the jacket.
Vj = 0.0307 m^3 = Vol. of the jacket.
Dp = Density of the person.
Vp = 0.0649 m^3 = Vol. of the person.
Dw = 1000kg/m^3 = Density of water.

Mj+Mp = (Vj+Vp) * Dw
Mj+Mp = 0.0956m^3 * 1000kg/m^3=95.6 kg
Mj = 95.6 - Mp = 95.6 - 70.3 = 25.3 kg

Dj = Mj/Vj = 25.3/0.0956=264.6 kg/m^3 =
Density of the jacket.