Question

when designing a building, you must be sure that the building can withstand hurricane - force winds, which have a velocity of 74 mi/h or more. the formula $f = 0.004av^{2}$ gives the force $f$ in pounds exerted by a wind blowing against a flat surface. $a$ is the area of the surface in square feet, and $v$ is the wind velocity in miles per hour. how much force is exerted by a wind blowing at 85 mi/h against the side of the building shown? (there is an image of a building composed of a rectangle and a triangle. the rectangle has a length of 20 ft and a height of 14.5 ft. the triangle has a base of 20 ft and a height of 7.5 ft. not drawn to scale) options: about 5 tons, about 10.549 tons, about 53 tons, about 23 tons

Explanation:

Step1: Calculate area of the side

The side has a rectangular part (20ft×14.5ft) and a triangular part ($\frac{1}{2}×20ft×7.5ft$).
Area $A = (20×14.5) + (\frac{1}{2}×20×7.5) = 290 + 75 = 365$ sq ft.

Step2: Compute force in pounds

Use $F = 0.004Av^2$ with $A=365$, $v=85$.
$F = 0.004×365×85^2 = 0.004×365×7225 = 0.004×2637125 = 10548.5$ lbs.

Step3: Convert pounds to tons

1 ton = 2000 lbs.
Tons = $\frac{10548.5}{2000} ≈ 10.549$ tons.

Answer:

B. about 10.549 tons