Question

The resultant of two forces make 30° and 60° angles
with them and has magnitude 40 N. The magnitudes
of two vectors are :-

Answer 1

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Answer 2

Answer:

The magnitudes of two force vectors are $20\sqrt{3}N$ and $20N$

Explanation:

Given that,

The resultant of two forces make 30° and 60° angles with the two forces and has magnitude 40N and we are required to find the magnitude of both the vectors.

If a vector makes an angle $\theta$ with another vector then its magnitude is cosine of the angle times the magnitude of other vector.

Hence the magnitudes of the force vectors are

$|F_{1}|=Fcos30^{0}=40cos30^{0}=20\sqrt{3}N\\|F_{2}|=Fcos60^{0}=40cos60^{0}=20N$

Therefore,

The magnitudes of two force vectors are $20\sqrt{3}N$ and $20N$

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