Answer:
W = 46 J
Explanation:
We need to find the angle between the two vectors Force vector and displacement vector.
First we will find the angle α of the force vector
[tex]tan\alpha =\frac{1}{8} \\\\\\alpha =7.125 deg\\[/tex]
Then we find the angle β of the displacement vector
[tex]tan\beta=\frac{2}{6} \\\\beta = 18.43 deg\\[/tex]
With these two angles we can find the angle between the two vectors
∅ = α + β = 25.56 deg
The definition of work is given by the expression
[tex]W=F*d*cos (theta)[/tex]
The absolute value of F will be:
[tex]F=\sqrt{8^{2}+1^{2} } \\F= 8.06 N[/tex]
The absolute value of d will be:
[tex]d=\sqrt{(6 )^{2}+(2)^{2} } \\d= 6.32m\\[/tex]
Now we have:
[tex]W=8.06*6.32*cos(25.56)\\W=46 J[/tex]
