Question #82392

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Answer 1 · 2017-08-03T12:58:32

#|vec R| = 143.7N#
Angle between #100N# force and #vec R#=#tan^(-1)(57/282)#

#theta = # angle between vectors

#alpha# = angle between resultant and #F_1#

#F_1 = 100 N#

#F_2 = 50N#

Angle with vertical = #15^(o)#

#:. theta = 35^(o)#

Applying parallelogram law of vector addition,

#|vec R| = sqrt((F_1)^2 + (F_2)^2 + 2(F_1)(F_2)(cos theta))#

#rArr |vec R| = sqrt((100)^2 + (50)^2 + 2(100)(50)(cos 37^o))#

#rArr |vec R| = 30sqrt(23) N#

#rArr |vec R| = 143.7 N#

#tan alpha = (F_2sin theta)/(F_1 + F_2cos theta) #

#rArr tan alpha = (50sin35)/(100+50cos35) #

#rArr tan alpha = 28.5/141#

#rArr tan alpha = 57/282#

#rArr alpha = tan^(-1)(57/282)#