First slide

Motion in a plane

Question

The square of the resultant of two forces 4 N and 3 N exceeds the square of the resultant of the two forces by 12, when they are mutually perpendicular. The angle between the vectors is

Moderate

Solution

θ₁ = 90⁰, resultant is R₁
θ₂ = θ, resultant is R₂ and R₂² = R₁² +12
P²+Q² +2PQcosθ = P² +Q²+12
2PQcosθ = 12 ⇒ 2(4)(3)cosθ=12
cosθ=1/2 ⇒θ=60⁰

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