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#