Final answer:
To find the magnitude of the force opposing the movement of the boulder, we use the Pythagorean theorem and calculate the resultant force to be 120.4 N, which represents the opposing force keeping the boulder stationary.
Step-by-step explanation:
The question is asking about the magnitude of force opposing the movement of a boulder, given that two farm workers are applying forces in different directions without causing motion. To find this opposing force, we'll assume that since the boulder does not move, the net force on the boulder is zero. This situation illustrates equilibrium where the sum of all forces equals zero. The forces applied are at right angles (north and east), so we can use the Pythagorean theorem to find the resultant force that the workers collectively apply.
We calculate the resultant force (F) using the formula F = √(Fn2 + Fe2), where Fn is the force applied to the north (80.0 N) and Fe is the force applied to the east (90.0 N).
Then:
- F = √(80.02 + 90.02)
- F = √(6400 + 8100)
- F = √(14500)
- F = 120.4 N
Therefore, the magnitude of the opposing force that keeps the boulder stationary is 120.4 N.