A rectangular boat is 9 m wide and 6 m long.

Question

After a truck pulls onto the ferry, the boat ends up with a depth of 9 cm submerged under the water. What is the combined weight of the truck and the ferry? (Assume the density of water is 1000 kg/m3.)

Answer 1

Fb - mg = 0 : Sum all of the forces in the y-direction. There is an upward buoyant force (Fb) and a downward gravitational force (mg) which cancel each other out (because the object is floating).

Fb = mg : The two forces are equal to each other.

pgV = mg : The buoyant force of an object = (density of solution)(acceleration of gravity)(volume displaced)

pglwh = mg : The volume is equal to the length x width x depth of boat under water

(1000)(9.8)(6)(9)(.09) = mg = W(weight)

W = 47628 Newton