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the force exerted by the wind on a plane surface varies jointly with the square of the velocity of the wind and with the area of the plane surface. if the area of the surface is 1 square feet and the wind velocity is 80 miles per hour, the resulting force is 6 pounds. find the force on a surface of 4 square feet with a velocity of 40 miles per hour.

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The force on a surface of 4 square feet with a velocity of 40 miles per hour is 6 pounds.

To find the force on a surface of 4 square feet with a velocity of 40 miles per hour, we can use the equation provided. The force exerted by the wind on a plane surface varies jointly with the square of the velocity of the wind and with the area of the plane surface. If we let F represent the force, v represent the wind velocity, and A represent the area of the surface, then the equation can be written as:

F = k x v² x A

Where k is a constant of proportionality.

We can use the given information to solve for k. If the area of the surface is 1 square feet and the wind velocity is 80 miles per hour, the resulting force is 6 pounds. Substituting these values into the equation, we get:

6 = k x (80²) x 1

6 = k x 6400

k = 6/6400

k = 0.0009375

Now we can use this value of k to find the force on a surface of 4 square feet with a velocity of 40 miles per hour. Substituting these values into the equation, we get:

F = 0.0009375 x (40²) x 4

F = 0.0009375 x 1600 x 4

F = 0.0009375 x 6400

F = 6 pounds

Therefore, the force on a surface of 4 square feet with a velocity of 40 miles per hour is 6 pounds.

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