Question

One of the rectangular component of a vector of $20$ m is $10$ m . The other component is:

• A. $20m$
• B. $2\sqrt{3}m$
• C. $10\sqrt{3}m$
• D. None of these

Answer 1

The correct option is C $10\sqrt{3}m$

Let $A_X=Acos\theta =20cos\theta =10$
$\Rightarrow cos\theta =\frac{1}{2}$
$\theta ={60}^{\circ }$
so, $A_Y=Asin\theta =20sin{60}^{\circ }=10\sqrt{3}$
Alternatively,
$A_Y=\sqrt{A^2-A_X^2}=\sqrt{{20}^2-{10}^2}=\sqrt{300}=10\sqrt{3}$