Question

If $F_1=10\text{N}$ and $F_2=20\text{N}$ as shown in the figure, the resultant $R$ will be [Hint: $\cos {65}^{\circ }=0.423$]

• A. $15.87\text{N}$
• B. $35.87\text{N}$
• C. $25.87\text{N}$
• D. $20.87\text{N}$

Answer 1

The correct option is C $25.87\text{N}$

From the question, the angle between the force vectors is
$\theta ={90}^{\circ }-{15}^{\circ }-{10}^{\circ }={65}^{\circ }$
Therefore, resultant is
$R=\sqrt{F_1^2+F_2^2+2F_1{F}_2\cos \theta }$
$\Rightarrow R=\sqrt{{10}^2+{20}^2+2\times 10\times 20\times \cos {65}^{\circ }}$
$\Rightarrow R=\sqrt{100+400+400\times 0.423}=25.87\text{N}$