Question

the resultant of two forces P and Q acting at an angle theta is (2m+1) √p² + q² . when the act and angle ( 90 - θ ) , the resultant is ( 2 m -1 ) √p² + q². find TANθ
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Answer 1

Answer

the picture gives you the step by step explanation for the given problem.

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Answer 2

Solution

Here, {(2m + 1) (√P2 + Q2}2 = P2 + Q2 + 2PQ cos θ and

{(2m – 1) (√P2 + Q2)}2 = P2 + Q2 + 2PQ cos (90 – θ)

(2m + 1)2 (P2 + Q2) – (P2 + Q2) = 2PQ cos θ —- (i)

(2m – 1)2 (P2 + Q2) – (P2 + Q2) = 2PQ sin θ —- (ii)

Taking ratio (ii) by (i),

tan θ = {[(2m – 1)2 – 12] [P2 + Q2]} / {[(2m + 1)2 – 12] [P2 + Q2]}

tan θ = [m – 1] / [m + 1]

hope this will help you