Question

Two forces of magnitude P & 3​ P act at right angles to each other Their resultant makes an angle θ with P. Which of the following gives the correct value of θ?

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Answer 1

Given the two forces with magnitudes P and 3P are acting at right angles.

Let Pₙ be the resultant force of the other two forces.

WKT, Pₙ = √[(P² + (3P)² + 2(P)(3P)cos(90)]

Pₙ = √10P² = √(10)P

We can find out the angle between P and 4P with α=tan⁻¹(Bsin(90)/A+Bcos(90))

α = tan⁻¹( √10P / P)

α = tan⁻¹(√10)

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