Answer
The work done is 22.05 foot-pounds.
Work Step by Step
Here, the force can be resolved into two vectors, such that:
$\mathbf{F}=\left( 4\cos 50{}^\circ,4\sin 50{}^\circ \right)$ …… (1)
As, the object is moved from point $\left( 3,7 \right)$ to $\left( 8,10 \right)$, therefore, the point to which the object has traveled is:
$\begin{align}
& \mathbf{AB}=\left[ \left( 8,10 \right)-\left( 3,7 \right) \right] \\
& =\left[ \left( 8-3 \right),\left( 10-7 \right) \right] \\
& =\left( 5,3 \right)
\end{align}$
$\mathbf{AB}=5\mathbf{i}+3\mathbf{j}$ …… (2)
Now, as it is known that:
$\mathbf{W}=\mathbf{F}\cdot \mathbf{AB}$ …… (3)
Substituting equation (1) and (2) in equation (3),
$\begin{align}
& \mathbf{W}=\left( 4\cos 50{}^\circ,4\sin 50{}^\circ \right)\cdot \left( 5,3 \right) \\
& =\left[ \left( 4\cos 50{}^\circ \times 5 \right)+\left( 4\sin 50{}^\circ \times 3 \right) \right] \\
& =20\cos 50{}^\circ +12\sin 50{}^\circ \\
& \approx 22.05
\end{align}$
