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The problem in the image deals with calculating the force exerted by waves on a protective wall and selecting materials based on that force. The equation provided for the power (P) exerted by the wave on the wall is:

\[
P = \frac{1}{2} \rho v^2
\]

Where:
- $ \rho $ (rho) is the density of the water (not specified, but typically taken as 1000 kg/m³ for seawater).
- $ v $ is the velocity of the waves, given as $ 900 \, \text{km/h} $.

The image also includes a table to help select materials based on the range of power and the corresponding price per square kilometer.

To solve the problem, we will:

1. Convert the velocity from $ \text{km/h} $ to $ \text{m/s} $.
2. Plug in values to calculate the power $ P $.
3. Based on the calculated power, select the appropriate material from the table.

Let's begin the calculation by converting velocity.

\[
v = 900 \, \text{km/h} = \frac{900 \times 1000}{3600} \, \text{m/s}
\]

Let me compute that first.The velocity of the wave is $ 250 \, \text{m/s} $.

Now, using the formula $ P = \frac{1}{2} \rho v^2 $ with $ \rho = 1000 \, \text{kg/m}^3 $ (the density of water), we can calculate the power exerted by the wave on the wall. Let's compute the power.The power exerted by the wave on the wall is $ 31,250,000 \, \text{P} $.

However, it seems that the table lists power ranges in units of $ 100,000 \, \text{P} $, so we can express this as:

\[
P = \frac{31,250,000}{100,000} = 312.5 \, \text{P}
\]

This places the power in the range of 300,000P to 400,000P. Therefore, based on the table, the appropriate material for the wall construction would be **Material B**, which costs $2500 per square kilometer.

Would you like to proceed with further calculations, such as the cost estimate or any clarifications?

Here are five related questions:
1. How is the power of a wave typically measured in real-world scenarios?
2. What role does the density of the water play in determining the power exerted by the wave?
3. How does the height of the wave affect the structural requirements of the wall?
4. Why is a special coating applied to the wall, and how does it affect the total cost?
5. How would the required material change if the velocity of the wave were higher?

**Tip**: Always ensure units are consistent when applying formulas, especially in physics problems involving velocity and energy!

A village is protected by a wall from very large waves. The waves can reach a maximum height of 10 km with a velocity of 900 km/h. The power (P) exerted by the waves on the wall is calculated using the formula P = (1/2)ρv², where ρ is the density of the water (assumed 1000 kg/m³). Based on the power, the material for the wall should be chosen from a table that lists materials and their corresponding costs per square kilometer.

Learn how to calculate the force exerted by a wave on a protective wall using the formula P = (1/2)ρv². The problem involves selecting the appropriate wall material based on the power exerted, with wave velocity of 900 km/h and water density of 1000 kg/m³. Suitable for students in Grades 10-12.

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