Three boys are pulling a heavy trolley by means of three ropes. The boy in the middle is exerting a pull of `100N`. The other two boys ,whose ropes both make an angle `30^(@)` with the central rope, are pulling with forces of `50sqrt(3)N` and `100sqrt(3)N`. Find the magnitudes of the resultant pull on the trolley.

Answer

327.9 N

Explanation

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`