Answer:
The bottom of the boat is submerged 0.07m
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:
[tex]V=length*width*height[/tex]
where the height is the depth that is the boat submerged, and is the information that we need to find, so
[tex]d=\frac{m}{V}[/tex]
solving for V:
[tex]V=\frac{m}{d}[/tex]
replacing the volume in terms of its measures:
[tex]length*width*height=\frac{m}{V}[/tex]
solving for the height:
[tex]height=\frac{m}{d*length*width}[/tex]
Finally you should replace the values:
[tex]height=\frac{200kg+257kg}{1000\frac{kg}{m^{3}}*4.53m*1.42m}[/tex]
[tex]height=\frac{457kg}{6432.6\frac{kg}{m}}[/tex]
[tex]height:0.07m[/tex]
As we said before, this is the height at which the boat is submerged.
