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Sagot :
Solution :
c). [tex]$\vec{F}_A = $[/tex] force applied by Abe
[tex]$\vec{F}_B = $[/tex] force applied by Barry
[tex]$\vec{F}_E = $[/tex] force applied by Eric
[tex]$\vec{F}_R = $[/tex] Resultant force
[tex]$\vec{F}_A $[/tex] in the vector form can be written as :
[tex]$\vec{F}_A = 0 \hat{i} + 60 \hat{j}$[/tex]
[tex]$\vec{F}_B $[/tex] in the vector form can be written as :
[tex]$\vec{F}_B = 60 \hat{i} + 0 \hat{j}$[/tex]
The resultant,
[tex]$\vec{F}_R= \vec{F}_A+\vec{F}_B $[/tex]
[tex]$=(0 \hat i + 60 \hat j)+(60 \hat i + 0\hat j)$[/tex]
[tex]$=60 \hat i + 60 \hat j$[/tex]
[tex]$|\vec{F}_R| = \sqrt{60^2+60^2}$[/tex]
= 84.853 N
d). As the three forces are in equilibrium, therefore,
[tex]$|\vec F_E| = |\vec F_R|$[/tex]
[tex]$|\vec F_E| =84.853 \ N$[/tex]
e). The direction of the force exerted by Eric is exactly opposite to the direction of the resultant force.
The direction of the resultant force is :
[tex]$\theta = \tan ^{-1}\left(\frac{F_y}{F_x}\right)$[/tex]
[tex]$ = \tan ^{-1}\left(\frac{60}{60}\right)$[/tex]
= 45° north east
The direction of the force E is 45° west or 45° south west.

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