Answer
The work done is 40 foot-pounds
Work Step by Step
Here, the object moves along the straight line, such that the angle between the force and direction of motion is ${{0}^{\circ }}$.
The object is moved from point $\left( 4,9 \right)$ to $\left( 10,20 \right)$. Therefore, the point to which the object has traveled is:
$\begin{align}
& \mathbf{AB}=\left[ \left( 10,20 \right)-\left( 4,9 \right) \right] \\
& =\left[ \left( 10-4 \right),\left( 20-9 \right) \right] \\
& =\left( 6,11 \right)
\end{align}$
$\mathbf{AB}=6\mathbf{i}+11\mathbf{j}$ …… (2)
Now, as it is known that:
$\mathbf{W}=\mathbf{F}\cdot \mathbf{AB}$ …… (3)
Substituting equation (1) and (2) in equation (3),
$\begin{align}
& \mathbf{W}=\left( 3\mathbf{i}+2\mathbf{j} \right)\left( 6\mathbf{i}+11\mathbf{j} \right) \\
& =\left[ \left( 3\times 6 \right)+\left( 11\times 2 \right) \right] \\
& =18+22 \\
& =40
\end{align}$
