Question

The resultant of two forces having magnitude $8\text{N}$ and $15\text{N}$ is $17\text{N}$. Find the angle between forces of $8\text{N}$ and $15\text{N}$.

• A. ${30}^{\circ }$
• B. ${60}^{\circ }$
• C. ${90}^{\circ }$
• D. ${45}^{\circ }$

Answer 1

The correct option is C ${90}^{\circ }$

Let $|\overrightarrow{R}|=17\text{N}$
$|\overrightarrow{P}|=8\text{N}$
$|\overrightarrow{Q}=15\text{N}$.
also,
$|\overrightarrow{R}|=\sqrt{P^2+Q^2+2PQ\cos \theta }$
$17=\sqrt{8^2+{15}^2+2\times 8\times 15\cos \theta }$
or, ${17}^2=8^2+{15}^2+240\cos \theta$
or, $289=289+240\cos \theta$
or, $\cos \theta =0$
or, $\theta ={90}^{\circ }$