Question

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?

Answer 1

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.