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

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:

$V=length*width*height$

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

$d=\frac{m}{V}$

solving for V:

$V=\frac{m}{d}$

replacing the volume in terms of its measures:

$length*width*height=\frac{m}{V}$

solving for the height:

$height=\frac{m}{d*length*width}$

Finally you should replace the values:

$height=\frac{200kg+257kg}{1000\frac{kg}{m^{3}}*4.53m*1.42m}$

$height=\frac{457kg}{6432.6\frac{kg}{m}}$

$height:0.07m$

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