A boat (with a flat bottom) and its cargo weigh 8,000 N. The area of the boat's bottom is 5 m2. How far below the surface of the water is the boat's bottom when it is floating in water? Find m

Question

A boat (with a flat bottom) and its cargo weigh 8,000 N. The area of the boat's bottom is 5 m². How far below the surface of the water is the boat's bottom when it is floating in water? Find m

Answer 1

Buoyant force = weight of water displaced by boat

Buoyant force = 8000 N

If d is the depth in m, then volume of water displaced is 5d m³

1 m³ water has mass 1000 kg, so weight 1000 x 9.8 = 9800 N

So 8000 = 5d x 9800 giving d = 0.1632 m

As data (8000, 5, 9.8) has min 1 significant figure give answer to 1 sf, ie 0.2m.