A flatbottomed boat with vertical sides has dimensions of 10

A flat-bottomed boat with vertical sides has dimensions of 10 foot times 4 feet (Boat A) and is floating in a lake next to a similar massed boat that is 8 feet times 5 feet (Boat B) Which boat has a greater draft (depth below the surface)?

Solution

Data:

Bottom area for boat A , A1 = 10 x 4 = 40 sq.ft

Bottom area for boat B , A2 = 8 x 5 = 40 sq.ft

Mass of boat A = Mass of boat B = M

Now, we know that the weight of the boat is balanced by the buoyant force of the water displaced

i.e., Weight of fluid displaced = Weight of boat

Density of water x Volume of water displaced = M

x A x d = M

i.e. d = M / ( x A)

where, d = depth of boat below surface / draft

A = area of the bottom the boat,

M =mass of the boat

Now, it is evident from the equation above, that for two boats of equal mass the draft will depend upon the bottom area.

Answer: In our case, as the bottom area for both boats A and B is exactly the same, the draft will also be the same.