Step 1 : Understanding the Question:
In this problem, we analyze the effect of a force applied at an angle to a horizontal plane. Since the force is not directed purely horizontally, only a portion of its magnitude is effective in causing horizontal acceleration. We are instructed to ignore friction, meaning there are no opposing forces acting along the horizontal axis. Our goal is to determine the horizontal acceleration of the mass by finding the net horizontal force.
Step 2 : Key Formulas and Approach:
We use vector resolution to isolate the component of the force acting along the horizontal direction:
\[
F_x = F \cos\theta
\]
Once the horizontal force component is obtained, we utilize Newton's Second Law of Motion to solve for the resulting acceleration of the object:
\[
a = \frac{F_{\text{net}}}{m}
\]
Our plan is to resolve the force vector horizontally and then divide this component by the object's mass.
Step 3 : Detailed Solution:
Identify and write down the given physical values: force \( F = 20 \text{ N} \), mass \( m = 5 \text{ kg} \), and angle \( \theta = 60^{\circ} \).
Compute the horizontal component of the force using the cosine of the given angle:
\[
F_x = F \cos 60^{\circ}
\]
Substitute the standard trigonometric value \( \cos 60^{\circ} = \frac{1}{2} \) into the formula:
\[
F_x = 20 \times 0.5 = 10 \text{ N}
\]
Apply Newton's Second Law along the horizontal axis to calculate the acceleration:
\[
a = \frac{F_x}{m} = \frac{10 \text{ N}}{5 \text{ kg}} = 2 \text{ m/s}^2
\]
Step 4 : Final Answer:
The horizontal acceleration of the object is \( 2 \text{ m/s}^2 \), which corresponds to option (A).
\[
\boxed{2\text{ m/s}^2}
\]