Magnitude and angle made with larger force?

Two forces 429 N and 591 N act on an object. The angle between the forces is 46°.

Find the magnitude of the resultant and the angle that it makes with the larger force .

Thank you friends

1 Answer
A08
Mar 14, 2018

Two vectors #Phati and vecQ# having an angle #theta#
Magnitude of Resultant Vector

#vecR= sqrt(P^2 + Q^2 + 2PQcos theta)#
#=>vecR= sqrt(591^2+429^2 + (2xx591xx429xxcos 46^@))#
#=>vecR= sqrt(349281+184041 + 352246)#
#=>vecR= 941\ N#

Taking #hati# along larger vector, the direction of Resultant Vector

#alpha= tan^-1 [(Q sin theta) / (P + Q cos theta)]#
#=>alpha= tan^-1 [(429 xx sin 46^@) / (591+429 xx cos 46^@)]#
#=>alpha= tan^-1 [308.6 / 889.0]#
#=>alpha= 19.1^@#

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