Question

A 75.5-kg person puts on a life jacket, jumps into the water, and floats. The jacket has a volume of 3.38 x 10-2 m3 and is completely submerged under the water. The volume of the person's body that is underwater is 6.42 x 10-2 m3. What is the density of the life jacket?

Answer 1

Density of jacket will be
`680.4733kg/m^3`

Step-by-step explanation:

We know that weight of water displaced= buoyant force=weight of man

Now volume of water displaced
`v=3.38* 10^(-2)+6.42* 10^(-2)=9.8* 10^(-2)m^3`

Density of water
`d=100kg/m^3`

So weight of water displaced
`=9.8* 10^(-2)* 1000=98kg`

So weight of jacket = 98-75 = 23 kg

We have given volume of the jacket =
`3.38* 10^(-2)m^3`

So density of jacket
`=(mass)/(volume)=(23)/(3.38* 10^(-2))=680.4733kg/m^3`