A man whose weight is 667 N and whose density is 980kg/m 3 can float in water wi

Question

A man whose weight is 667 N and whose density is 980kg/m3 can float in water with his head above the surfacewith the help of a five jacket which is wholly immersed. Assumingthat the volume of his head is 1/15 of his whole volume and thatthe denisty of the life jacket is 250 kg/m3, find thevolume of the life jacket. Thanks for the help A man whose weight is 667 N and whose density is 980kg/m3 can float in water with his head above the surfacewith the help of a five jacket which is wholly immersed. Assumingthat the volume of his head is 1/15 of his whole volume and thatthe denisty of the life jacket is 250 kg/m3, find thevolume of the life jacket. Thanks for the help

Explanation / Answer

the volume of the man : V = m/ = W/g = 0.06945 m3 => volume under the water level : V1 = (14/15)V = 0.06482m3 Let V2 be the volume of the jacket,we have : W + W(jacket) = o*g*(V1 + V2) => W + (jacket)*g*V2 = o*g*(V1+ V2) => V2 = (W - o*g*V1)/(g(o - (jacket))) =(667 - 1000*9.8*0.06482)/(9.8*(1000-250)) = 4.32x10^-3 m3

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