A tourist to the Dead Sea finds that he is able to float on

A tourist to the Dead Sea finds that he is able to float on the water due to the high salt content, making the water denser than fresh water. The specific gravities of the salt water and person are 1.17 and 1.025, respectively. The person is 5 ft 11 in tall, has a shoulder width of 18 in, and a head of diameter 7 in. If this tourist were to take a dip in the sea, what percentage of his body volume would be below the water surface when he is floating? 87.6%

Solution

By applying Archimedes principle of bouyancy states that the bouyancy force on an object is equal to the weight of the fluid displaced by the object.

By Archimedes\' principle, the weight of water displaced is mwg, so the buoyant force is

We can calculate the density proportion of the object to water by