The resultant of two forces has magnitude of 20N. If one of the forces is of magnitude 20√3 N and makes an angle of 30o with the resultant, then the other forces must be of magnitude:
Correct answer: B. 20 N
- A. 10√3 N
- B. 20 N
- C. 20√3 N
- D. 10 N
- E. 37 N
Explanation
Take the resultant along the x-axis: R = (20, 0) N. The known force 20√3 N at 30° to R is (20√3·cos30°, 20√3·sin30°) = (30, 10√3) N. The other force = R − (30, 10√3) = (−10, −10√3) N, whose magnitude is √(10² + (10√3)²) = √(100 + 300) = √400 = 20 N.
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