Answer
a) See the detailed answer below.
b) See the figure below.
c) $a_x=2.87\;\rm m/s^2$
Work Step by Step
a) A 20-kg box is attached to a wire and the wire is making an angle of 30$^\circ$ above the horizontal. The other end of the wire is attached to a worker who pulls the box forward by a force of 100 N. If you know that the coefficient of kinetic friction between the box and the ground is 0.20, find the box's acceleration.
b) See the figure below.
c) From the first given formula
$$a_x=\dfrac{100\cos30^\circ-f_k}{20}$$
Plugging $f_k$ from the last given formula (the third one);
$$a_x=\dfrac{100\cos30^\circ-0.2n}{20}\tag 1$$
Now we need to find the normal force, so we can use th second given formula.
$$n=(20\cdot 9.8)-100\sin30^\circ=146\;\rm N$$
Plugging into (1);
$$a_x=\dfrac{100\cos30^\circ-0.2\cdot 146}{20}=\color{red}{\bf 2.87}\;\rm m/s^2 $$
