10. The resultant of two forces has magnitude 20 N. One of the forces is of magnitude 20√3 N and makes an angleof 30° with the resultant. Then what is the magnitude ofthe other force?
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10. The resultant of two forces has magnitude 20 N. One of the forces is of magnitude 20√3 N and makes an angleof 30° with the resultant. Then what is the magnitude ofthe other force?
need steps...
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Answer:-
Given:
Magnitude of resultant of two forces (R) = 20 N
Magnitude of first force (A) = 20√3
Angle between A & R = 30°
Let the magnitude of other force be B.
We know that,
R = √(A² + B² + 2ABcos ∅)
According to the question,
→ B = √(A² + R² + 2ARcos 30°)
→ B = √(20√3)² + (20)² + 2 * 20√3 * 20 * √3/2
→ B = √(1200 + 400 + 1200)
→ B = √2800
→ B = √7 * √400
→ B = 20√7 N
Therefore, the magnitude of other force will be 20√7 N.