Final answer:
The acceleration of the box is found by calculating the horizontal component of the applied force and utilizing Newton's second law. The calculation results in 2.5 m/s², which does not match any of the provided answer options, suggesting an error in the available choices.
Step-by-step explanation:
To determine the acceleration of the box, we first need to consider the component of the applied force that will contribute to the horizontal motion of the box since the floor is frictionless. The applied force is 20 N at an angle of 60 degrees above the horizontal, so we use the cosine function to find the horizontal component of this force:
Fhorizontal = 20 N × cos(60°) = 20 N × 0.5 = 10 N
Next, we use Newton's second law, which states that Force = mass × acceleration (F = ma). The weight of the box is given as 39.2 N; we can find the mass by dividing the weight by the acceleration due to gravity (g = 9.8 m/s²):
mass = 39.2 N / 9.8 m/s² = 4.0 kg
Now we can find the acceleration by rearranging Newton's second law to solve for 'a':
a = Fhorizontal / mass = 10 N / 4.0 kg = 2.5 m/s²
This acceleration value is not listed in the provided answer options, indicating a possible error in either the question itself or the provided answer choices. Based on the calculation, the correct answer for the acceleration of the box would be 2.5 m/s².