Question

two boys raising a load pull at an angle to each other. if they exert forces of 30N and 60N respectively and their effective pull is at right angles to the direction of the pull of the first boy, what is the angle between their arms? what si the effective pull?

Answer 1

$$\begin{gathered} ForcebyfirstboyisA=30N \\ forcebysecondboyisB=60N \\ resul\tan tforceisR \\ R=\sqrt{A^2+B^2+2AB\cos \theta } \\ angleoftheresul\tan tforcewithforceappliedbyfirstboyis90 \\ \tan 90=\frac{B\sin \theta }{A+B\cos \theta } \\ \infty =\frac{\mathbf{B}\mathbf{sin}\mathbf{\theta }}{\mathbf{A}\mathbf{+}\mathbf{B}\mathbf{cos}\mathbf{\theta }} \\ \mathit{A}\mathbf{+}\mathit{B}\mathbf{cos}\theta =0 \\ A=-B\cos \theta \\ \cos \theta =\frac{-A}{B}=\frac{-1}{2} \\ \theta ={120}^o \\ R=\sqrt{{30}^2+{60}^2+2\times 30\times 60\times \cos 120} \\ R=51.96N \\ thisistheeffectivepull. \end{gathered}$$