Answer :
Final answer:
The second force that maintains equilibrium with the first must have the same magnitude of 35.8 N and a direction of -147.2 degrees counterclockwise from the positive x-axis. This results in the second force being exactly opposite in direction to the first force, making option B the correct answer.
Explanation:
The student's question involves understanding the equilibrium of forces and vector addition. Given that the velocity of the object does not change, the forces acting on it must be balanced, meaning that they are equal in magnitude and opposite in direction. The first force is 35.8 N at 212.8 degrees counterclockwise from the positive x-axis. The second force must therefore have the same magnitude but be directed in the opposite direction to maintain equilibrium. Since the given angle is more than 180 degrees, we subtract it from 360 degrees to find the direction of the second force, which gives us 147.2 degrees. However, the question asks for the angle to be between 180 and -180 degrees; thus, we represent this direction as -147.2 degrees (360 - 212.8 = 147.2, and -360 + 212.8 = -147.2).
So the correct answer is: Magnitude: 35.8 N, Direction: -147.2 degrees, which corresponds to option B.
