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A 200-kg flat-bottomed boat floats in fresh water, which has a density of 1000 kg/m3. If the base of the boat is 1.42 m wide and 4.53 m long, to what depth is the bottom of the boat submerged when it carries three passengers whose total mass is 257 kg?

User Goni
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Answer:

The bottom of the boat is submerged 0.07m

Step-by-step explanation:

For this problem you should take in consideration the Archimedes´ principle, that states that the volume of a submerged object is equal to the volume of the displaced water.

In this case the problem gives you the information about length and width and also says that is a flat-bottomed boat, so you can calculate the volume as:


V=length*width*height

where the height is the depth that is the boat submerged, and is the information that we need to find, so


d=(m)/(V)

solving for V:


V=(m)/(d)

replacing the volume in terms of its measures:


length*width*height=(m)/(V)

solving for the height:


height=(m)/(d*length*width)

Finally you should replace the values:


height=(200kg+257kg)/(1000(kg)/(m^(3))*4.53m*1.42m)


height=(457kg)/(6432.6(kg)/(m))


height:0.07m

As we said before, this is the height at which the boat is submerged.

User Jeferson Macedo
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