Solution to Riddle of the Week

Solution to Riddle of the Week: A Boat, a Brick, and a Tricky Question

Difficulty level: Moderate

By Jay Bennett

Any sailors reading this riddle certainly had no trouble with it, and the same principle here applies to throwing an anchor overboard. Think about what the brick is doing while it is in the boat. You can check the original question here.

SOLUTION

The water level goes down. The reason is that the mass of the brick while its in the boat displaces more water, compared to the volume of the brick when it is submerged in the water. This might seem counterintuitive at first, but some quick physics can show us why it's true.

You probably remember from middle school science that an object submerged in water displaces the water equal to its volume. You put a brick-sized object in a pool and it displaces a brick-sized amount of water. However, when an object floats on top of the water because it's buoyant—that is, its density is lower than the density of water (1 g/cm³), then it's a different story. The displacement of the water is equal to the mass of the floating object. This is true for the boat, and it is true for the boat with the brick in it.

You know that a brick sinks. The reason it does is that the density of the brick is higher than the density of the water. This also tells us that the volume of water needed to equal the mass of the brick is larger than the volume of the brick. Think of it this way: How much water would you need to equal the weight of a brick? It's definitely more than would fit in a container with the same volume as the brick.

So when the brick is in the boat, it is pushing the boat down and displacing water equal to its mass. And when you hurl the brick into the water, it displaces the water equal to its volume.

Just for fun, let's put some numbers on this. A standard brick measures 9.2 cm x 5.7 cm x 20.3 cm, which is a volume of 1064.5 cm³. That's how much water is displaced when the brick is thrown into the lake. A standard brick has a mass of about 2 kg, which is equal to 2 L of water, which is equal to 2,000 cm³. That's how much water is displaced when the brick is in the boat. More water is displaced when the brick is in the boat, and the water level is higher, but once you toss it into the lake, the displacement is less, and the water level drops.