Given: Force 12N and 14N
To Determine: The strength and the direction of the resultant
Solution
The strength of the given is the magnitude of the resultant
The result is R in the diagram above
Using Pythagoras theorem
[tex]\begin{gathered} R^2=12^2+14^2 \\ R^2=144+196 \\ R^2=340 \\ R=\sqrt{340} \\ R=2\sqrt{85}N \\ R=18.439N \end{gathered}[/tex]
From the diagram
[tex]\begin{gathered} tan\theta=\frac{12}{14} \\ tan\theta=\frac{6}{7} \\ \theta=tan^{-1}(\frac{6}{7}) \\ \theta=40.6^0 \end{gathered}[/tex]
The direction of the resultant is
[tex]Direction-of-the-resultant=90^0+40.6^0=130.6^0[/tex]
Hence:
The strength of the resultant is 18.4N
The direction of the resultant is 130.6⁰
