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?

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Answer 1 · 2018-08-10T15:45:39

$100N$

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 $alpha=90^@$

so, we can say, $R^2 =X^2 +Y^2 +2XY cos 90$

or, $200^2 =X^2 +Y^2....................1$

If,the $vec X$ makes an angle of $theta=60^@$ then,

we can write,

$tan theta = (Y sin alpha)/(X + Y cos alpha)$

putting the given values we find, $tan 60=Y/X$

or, $Y=sqrt(3)X...................2$

Putting $Y=sqrt(3)X$ in $1$ we get,

$X^2 +(sqrt(3)X)^2 =200*200$

or, $4X^2 =200*200$

or, $X^2=50*200=100*100$

or, $X=100N$