Answer
(c) is the correct answer.
Work Step by Step
Let's rewrite the forces in unit-vector notation, taking due east to be $+i$ and due north to be $+j$ direction.
$\vec{F}_1=-(12N)j$
$\vec{F}_2=-(17N)i$
So, $\sum \vec{F}=-(17N)i-(12N)j$
The object has mass $m=27kg$. According to Newton's 2nd Law, $$\vec{a}=\frac{\sum \vec{F}}{m}=-(0.63m/s^2)i-(0.44m/s^2)j$$
- Magnitude: $a=\sqrt{0.63^2+0.44^2}=0.77m/s^2$
- Direction: take $\theta$ to be the angle $\vec{a}$ makes with the horizontal
$$\tan\theta=\frac{0.44}{0.63}=0.698$$ $$\theta=35^o$$
Since $\vec{a}$ is in the 3rd quadrant, $\vec{a}$ is directed at an angle of $35^o$ south of west. (c) is correct.
