Question

The force of the wind blowing on a window positioned at a right angle to the direction of the wind varies jointly as the area of the window and the square of the wind's speed. It is known that a wind of 30 miles per hour blowing on a window measuring 4 feet by 5 feet exerts a force of 150 pounds. During a storm with winds of 60 miles per hour, should hurricane shutters be placed on a window that measures 3 feet by 4 feet and is capable of withstanding 300 pounds of force?

Answer 1

We have the following:

The force of wind: F = 150 pounds

The square of the winds speed: V = 30 miles per hour

The area of the windows: A = 4*5 = 20 square feet

The formula is:

$F=kAV^2$

replacing:

$\begin{gathered} 150=k\cdot20\cdot30^2 \\ k=\frac{150}{20\cdot900} \\ k=\frac{1}{120} \end{gathered}$

now, the force of wind with 60 miles per hour and 12 (3*4) square feet

$\begin{gathered} F=\frac{1}{120}\cdot12\cdot60^2 \\ F=360_{} \end{gathered}$

The answer is 360 pounds