Final answer:
After calculating the net force and the acceleration of the chair, the kinematic equation for distance traveled is used. The calculated distance of 13.39 meters doesn't match any of the provided options, suggesting the student should check the question or the options for errors.
Step-by-step explanation:
The student asks how far a chair will be pushed in 1.75 seconds if it is pushed forward with a horizontal force. To solve this, we must first find the net force acting on the chair by subtracting the frictional force from the applied force. The net force is then 138 N (185 N - 47 N). To find the acceleration, we use Newton's second law (F = ma).
The mass of the chair can be found using the gravitational force, which is 155 N downward and since the gravitational force is equal to the mass times the acceleration due to gravity (Fg = mg), the mass (m) is 15.82 kg (155 N / 9.8 m/s2). Using the net force and the mass, the acceleration (a) can be found: a = F/m which equals 8.73 m/s2 (138 N / 15.82 kg).
Now, with the acceleration and the time, we can determine the distance traveled using the kinematic equation s = ut + 1/2 at2, where s is distance, u is initial velocity (0 m/s), a is acceleration, and t is time. Substituting the known values gives s = 0 + 1/2 * 8.73 m/s2 * (1.75 s)2, which calculates to a distance of 13.39 meters.
However, the options provided in the question (a) 0.78 meters, (b) 2.00 meters, (c) 3.30 meters, and (d) 4.15 meters, do not include the calculated distance of 13.39 meters. Therefore, there seems to be a discrepancy in the provided choices. If this is a multiple-choice question and these are the only options given, the student should verify with the instructor or the source of the question for clarification, as none of the choices reflect the correct calculation based on the given information.