A boat floating in a water tank is carrying a number of large stones. If the stones are unloaded into water, what will happen to the water level?

Explanation

To solve the problem of what happens to the water level when stones are unloaded from a boat into a water tank, we can analyze the situation step by step.

### Step-by-Step Solution:

1. **Understanding the Initial Situation**:
- The boat is floating in a water tank and is carrying stones.
- The weight of the stones is supported by the buoyant force acting on the boat.

2. **Applying Archimedes' Principle**:
- According to Archimedes' principle, the buoyant force acting on an object submerged in a fluid is equal to the weight of the fluid displaced by that object.
- When the stones are in the boat, the boat displaces a volume of water equal to the weight of the boat plus the weight of the stones.

3. **Weight and Volume Relationship**:
- Let \( V_s \) be the volume of the stones and \( d_s \) be the density of the stones.
- Let \( V_l \) be the volume of the liquid displaced and \( d_l \) be the density of the liquid (water).
- The weight of the stones when they are in the boat is given by \( W_s = V_s \cdot d_s \).
- The weight of the water displaced by the boat is \( W_l = V_l \cdot d_l \).

4. **Equating the Weights**:
- Initially, when the stones are in the boat, the weight of the stones is equal to the weight of the water displaced:
\[ V_s \cdot d_s = V_l \cdot d_l \]
- Since the density of the stones \( d_s \) is greater than the density of water \( d_l \), it follows that:
\[ V_s < V_l \]
- This means the volume of stones is less than the volume of water displaced when the stones are in the boat.

5. **Unloading the Stones**:
- When the stones are unloaded from the boat and placed directly into the water, they will displace a volume of water equal to their own volume \( V_s \).
- Since the density of the stones is greater than that of water, the volume of water displaced by the stones \( V_s \) will be less than the volume of water that was displaced when the stones were in the boat \( V_l \).

6. **Conclusion**:
- Therefore, when the stones are unloaded into the water, the total volume of water displaced decreases.
- As a result, the water level in the tank will fall.

### Final Answer:
When the stones are unloaded into the water, the water level will **fall**.