Question

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 30 square feet surface and the wind velocity is 10 miles per hour, the resulting force is 20 pounds. Find the force, F, on a surface of 65 square feet with a velocityof 40 miles per hour.

Answer 1

Answer:

$693.33\text{ pounds}$

Step-by-step explanation:

Since, the formula of resulting force by Air,

$F=kv^2A$

Where,

v = velocity of wind,

A = surface area,

k = variation constant,

Here, F = 20 pounds, if, v = 10 miles per hour, A = 30 ft²

$\implies 20 = k(10)^2 (30)$

$20 = 3000k$

$\implies k = \frac{20}{3000}=\frac{1}{150}$

Now, if v = 40 miles per hour, A = 65 ft²,

Then the resultant force would be,

$F = \frac{1}{150}(40)^2(65)=\frac{1}{150}(1600)(65) = 693.33\text{ pounds}$