the wind blowing on a vertical surface varies jointly as the area of the surface and the square of the velocity. if a wind of 40 mph exerts a force of 50 pounds on a surface of 1/2 square foot , how much force will a wind of 80 mph place on a surface of 2 square feet

the equation is....

S=kwd(squared)

solve for k.

force/50= .5*40^2/(2*80^2)

To solve for k in the equation S = k * w * d^2, where S represents the force, w represents the wind velocity, and d represents the surface area, we can use the given information.

Given:
S1 = 50 pounds (force exerted by a wind of 40 mph on a surface of 1/2 square foot)
w1 = 40 mph
d1 = 1/2 square foot

Using these values in the equation, we have:

S1 = k * w1 * d1^2

50 = k * 40 * (1/2)^2
50 = k * 40 * 1/4
50 = k * 10
k = 50 / 10
k = 5

Now that we have determined the value of k, we can find the force exerted on a surface with a wind velocity of 80 mph and a surface area of 2 square feet (S2).

S2 = k * w2 * d2^2

Substituting the given values w2 = 80 mph and d2 = 2 square feet:

S2 = 5 * 80 * 2^2
S2 = 5 * 80 * 4
S2 = 1600 pounds

Therefore, a wind of 80 mph will place a force of 1600 pounds on a surface of 2 square feet.

To solve for k, we need to use the given information and plug it into the equation S = kwd^2, where S is the force exerted by the wind on the surface, w is the wind velocity, and d is the area of the surface.

Step 1: Given information
We know that when the wind velocity is 40 mph, the force exerted on the 1/2 square foot surface is 50 pounds.

So, S = 50 pounds, w = 40 mph, and d = 1/2 square foot.

Step 2: Substitute the values into the equation
50 = k(40)^2 * (1/2)

Step 3: Simplify the equation
50 = k * 1600 * 1/2
50 = 800k

Step 4: Solve for k
Divide both sides of the equation by 800:
50/800 = k
0.0625 = k

So, k is equal to 0.0625.

Now, let's use this value of k to find out the force exerted on a surface of 2 square feet when the wind velocity is 80 mph.

Given information:
w = 80 mph, d = 2 square feet

Using the equation S = kwd^2:
S = 0.0625 * 80^2 * 2
S = 0.0625 * 6400 * 2
S = 800

Therefore, the wind of 80 mph will exert a force of 800 pounds on a surface of 2 square feet.