Explanation:
Assumption: Supposing we have to find Force along the line [tex]y=\frac{1}{2}x[/tex] acting in the direction (2,2).
So, F in the direction (2,2)
[tex]F=\frac{30}{\sqrt{2^2+2^2}}=\frac{30\sqrt{2}}{2}[/tex]
The object is moving from point 0,0 to x, x/2. a distance of 3 feet. So, we can find the translation vector.(We must take the positive root since, we are in first quadrant.
[tex]x^2+\frac{x^2}{4}=3^2[/tex]
[tex]\Rightarrow 5x^2=36[/tex]
[tex]\Rightarrow x=\frac{6}{\sqrt{5}}=\frac{3(\sqrt{5}0}{5}[/tex]
therefore,
Work done W = F.x
[tex]=\frac{90\sqrt{10}}{10}(1+2)=27\sqrt{10}[/tex]
