Question

Two forces $\overrightarrow{A}=5\text{N}$ and $\overrightarrow{B}=2\text{N}$ makes an angle of ${60}^{\circ }$ with each other. Find the magnitude of resultant force.

• A. $10\text{N}$
• B. $3\text{N}$
• C. $\sqrt{29}\text{N}$
• D. $\sqrt{39}\text{N}$

Answer 1

The correct option is D $\sqrt{39}\text{N}$

Given:
$\overrightarrow{A}=5\text{N};\overrightarrow{B}=2\text{N}$ and $\theta ={60}^{\circ }$

Using Triangle Law of Vector addition,

$F_{res}=\sqrt{A^2+B^2+2AB\cos \theta }$

$F_{res}=\sqrt{5^2+2^2+(2\times 5\times 2)\cos {60}^{\circ }}$

$F_{res}=\sqrt{25+4+20\times \frac{1}{2}}=\sqrt{39}\text{N}$

Hence, option $\left(\text{B}\right)$ is correct.