A bouy is attached to three tugboats by three ropes. The tugboats are engaged in a tug-0f-war. One tugboat pulls west on the buoy with a force `vec(F)_(1)` of magnitude `1000N`. The second tugboat pulls south on the buoy with a force `vec(F)_(2)` of magnitude `2000N`. The third tugboat pulls northeast (that is, half way between north and east), with a force `vec(F)_(3)` of magnitude `2000N`
a. Express each force in unit vector from `(hat(i),hat(j))`.
b. Calculate the magnitude of the resultant force.

Answer

a.`x=vec(F)_(x)=1000(sqrt(2-1)hat(i)`; b. y= -1000(2-sqrt(2)) hat(j)`

Explanation

a.Resultant along `x=vec(F)_(x)=1000(sqrt(2)-1)hat(i)`
Along `y=vec(F)_(y)= -1000(2-sqrt(2))hat(j)`
b. `Fsqrt(F_(x)^(2)+F_(y)^(2))=1000(sqrt(2)-1) sqrt(3)N`