Question

a flat-bottomed boat has vertical sides and a bottom surface area of 0.75 m2. it floats in water such that its draft (depth below the surface) is 0.3 m. determine the mass of the boat. what is the draft when a 50-kg man stands in the center of the boat?

Answer 1

B = A H1 * D

Buoyant force on boat = Area * Sides * Density water

B = .75 m^2 * .3 m * 1000 kg/m^3 * 9.80 m/s^2 = 2200 N

B is buoyant force required to float boat

M = 2200 / 9.8 = 225 kg mass of boat

Volume of water required to float man

.75 m^2 * X2 * 1000 kg/m^3 = 50 kg

X2 = 50 / (.75 * 1000) = .067 m draft of boat supporting man

Check:

Mass of man / Mass of boat = 50 /225 = .22

Draft of man / Draft of boat = .067 / .30 = .22

Note: Total draft = .30 + .067 = .37 with man standing in boat