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

Answer:

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

Explanation:

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

Now volume of water displaced $v=3.38\times 10^{-2}+6.42\times 10^{-2}=9.8\times 10^{-2}m^3$

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

So weight of water displaced $=9.8\times 10^{-2}\times 1000=98kg$

So weight of jacket = 98-75 = 23 kg

We have given volume of the jacket = $3.38\times 10^{-2}m^3$

So density of jacket $=\frac{mass}{volume}=\frac{23}{3.38\times 10^{-2}}=680.4733kg/m^3$