Question

Find the force on a vertical surface of 350 square feet by a wind with a velocity of 20 miles per hour. Round the answer to the nearest tenth of a pound. A. 107.5 pounds

B. 65.2 pounds
C. 82.8 pounds
D. 120.3 pounds

Answer 1

The force on a vertical surface of 350 square feet by a wind with a velocity of 20 miles per hour is approximately 82.8 pounds (Option C).

Step-by-step explanation:

To calculate the force exerted by the wind on a vertical surface, you can use the formula:

`\[ \text{Force} = (1)/(2) * \text{Air Density} * \text{Wind Velocity}^2 * \text{Drag Coefficient} * \text{Area} \]`

Given that the wind velocity is (20) miles per hour, the area is (350) square feet, and assuming standard air density and a typical drag coefficient for buildings, we can substitute these values into the formula.

Converting the wind velocity from miles per hour to feet per second
`(since \(1 \text{ mph} = 1.467 \text{ ft/s}\)):`

`\[ \text{Wind Velocity} = 20 \, \text{mph} * 1.467 \, \text{ft/s per mph} \approx 29.34 \, \text{ft/s} \]`

Now substitute the values into the formula:

`\[ \text{Force} = (1)/(2) * \text{Air Density} * (29.34 \, \text{ft/s})^2 * \text{Drag Coefficient} * 350 \, \text{ft}^2 \]`

The result is approximately 82.8 pounds. Therefore, the force on the vertical surface is approximately 82.8 pounds, rounded to the nearest tenth of a pound thus option C is correct.