To express the gross weight [tex]\( w \)[/tex] of an aircraft as a function of its landing speed [tex]\( V \)[/tex], let's start with the given relationship:
[tex]\[ V = \sqrt{1.223 \, w} \][/tex]
1. First, isolate the square root by squaring both sides of the equation to remove the square root:
[tex]\[ V^2 = 1.223 \, w \][/tex]
2. Next, solve for [tex]\( w \)[/tex] by dividing both sides of the equation by 1.223:
[tex]\[ w = \frac{V^2}{1.223} \][/tex]
Thus, the equation that expresses the gross weight [tex]\( w \)[/tex] as a function of the landing speed [tex]\( V \)[/tex] is:
[tex]\[ w = \frac{V^2}{1.223} \][/tex]
Therefore, the correct option is:
D. [tex]\( w = \frac{V^2}{1.223} \)[/tex]
