Question

If one of the force is double of the other and resultant is equal to the greater force in magnitude then find out angle between both the forces?​

Answer 1

$Let \\ A = a \\B = 2a \\ R = 2a$

$R = \sqrt{ {a}^{2} + {b}^{2} + 2ab \cos\theta}$ $Now \\ According\:To\:Question\\2a =\sqrt{{(a)}^{2}+{(2a)}^{2}+2\times a \times2acos\theta}\\2a =\sqrt{{a}^{2}+{4a}^{2} + 4 {a}^{2}cos\theta}\\2a =\sqrt{{5a}^{2}+{4a}^{2}cos\theta}\\4{a}^{2} ={5a}^{2}+{4a}^{2}cos\theta\\- 4 {a}^{2}cos\theta =5 {a}^{2} - 4 {a}^{2} \\- 4 {a}^{2}cos\theta ={a}^{2} \\ cos\theta =\frac{ {a}^{2} }{ - 4 {a}^{2} } \\ cos\theta =-\frac{1}{4} \\\theta ={cos}^{-1} (-\frac{1}{4})$

Answer 2

Hey there

refer to attachment