Answer:
The work done to move the object is 27 ft-lbs
B is correct.
Step-by-step explanation:
A 4-lb. force acting in the direction of (4, -2).
First we find the unit vector of direction of force.
[tex]\hat{a}=\dfrac{4i}{\sqrt{20}}-\dfrac{2j}{\sqrt{20}}[/tex]
4-lb force acting in direction of vector a
[tex]\vec{F}=\dfrac{4}{\sqrt{20}}(4i-2j)[/tex]
Object move 7 ft from point (0,4) to (5,-1)
Displacement vector whose length 7 ft
[tex]\vec{r}=\dfrac{7}{\sqrt{50}}(5i-5j)[/tex]
Now, we will find workdone by force
[tex]W=\vec{F}\cdot \vec{r}[/tex]
[tex]W=\dfrac{4}{\sqrt{20}}(4i-2j)\cdot \dfrac{7}{\sqrt{50}}(5i-5j)[/tex]
[tex]W=\dfrac{28}{\sqrt{1000}}(20+10)[/tex]
[tex]W=26.56\approx 27\text{ ft-lbs}[/tex]
Hence, The work done to move the object is 27 ft-lbs
