A ferry boat has an internal volume of 1 m ^3 and a weight of 50 kg . If a leak develops in the bottom and water begins coming in, what fraction of the boat's volume will be filled with water before water starts coming in from the sides?

Step-by-step solution

Let V be the total volume of the boat and m be its mass. When water starts coming in from the sides, the boat is completely submerged. The volume of water displaced is equal to the total volume of the boat, V = 1 m ^3 . The buoyant force acting on the boat is F_B = V _w g , where _w = 1000 kg/m ^3 is the density of water. For the boat to just float, the total weight of the boat and the water inside it must equal the buoyant force. Let V_ in be the volume of water inside the boat. m g + V_ in _w g = V _w g Substitut