3 boys are pulling a heavy trolley by me...

`3` boys are pulling a heavy trolley by means of `3` ropes. The boy in the middle is exerting a pull of `100 N`. The other `2` boys, whose ropes both make an angle of `30^(@)` with the centre rope, are pulling with forces of `50 sqrt(3)N` & `100 sqrt(3)N`. Find the magnitude of the resultant pull the trolley. Consider all the forces in the same plane.

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The correct Answer is:

327.9 N

Resultant force in vertical direction

`=50sqrt(3) cos 30^(@)+100+100sqrt(3) cos 30^(@)`
`=50xx3/2+100+100xx3/2=325 N`
Resultant force in horizontal direction
`=100 sqrt(3) sin 30^(@)-50 sqrt(3) sin 30^(@)`
`100 sqrt(3)/2-(50sqrt(3))/2=25sqrt(3)N`
so resultant pull`=sqrt((325)^(2)+(25sqrt(3))^(2))=327.9 N`

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