Two forces whose resultant is 200N are perpendicular to each other. If one of them makes an angle of 60° with the resultant. Calculate it magnitude?

Aug 10, 2018

$100 N$

Explanation:

Suppose,one of the force is $\vec{X}$ and the other is $\vec{Y}$

so, $\vec{X} + \vec{Y} = \vec{R}$

where, $| \vec{X} | = X , | \vec{Y} | = Y , | \vec{R} | = 200$

again, angle between $\vec{X}$ and $\vec{Y}$ is $\alpha = {90}^{\circ}$

so, we can say, ${R}^{2} = {X}^{2} + {Y}^{2} + 2 X Y \cos 90$

or, ${200}^{2} = {X}^{2} + {Y}^{2.} \ldots \ldots \ldots \ldots \ldots \ldots .1$

If,the $\vec{X}$ makes an angle of $\theta = {60}^{\circ}$ then,

we can write,

$\tan \theta = \frac{Y \sin \alpha}{X + Y \cos \alpha}$

putting the given values we find, $\tan 60 = \frac{Y}{X}$

or, $Y = \sqrt{3} X \ldots \ldots \ldots \ldots \ldots \ldots .2$

Putting $Y = \sqrt{3} X$ in $1$ we get,

${X}^{2} + {\left(\sqrt{3} X\right)}^{2} = 200 \cdot 200$

or, $4 {X}^{2} = 200 \cdot 200$

or, ${X}^{2} = 50 \cdot 200 = 100 \cdot 100$

or, $X = 100 N$