Three tug boats are pulling on a cruise ship with three ropes. Two pull with a force of 1800 N each at angle of [N15°E] and [S24°E]. If the net force on the ship is zero, what must the tension in the third rope be?

Question

Three tug boats are pulling on a cruise ship with three ropes.  Two pull with a force of 1800 N each at angle of [N15°E] and [S24°E].  If the net force on the ship is zero, what must the tension in the third rope be?

Henry · Answer

F1 + F2 + F3 = 0
1800N[75o] + 1800N[294o] + F3 = 0
1800*cos75+i1800*sin75 + 1800*cos294+i
1800*sin294+F3 = 0, 465.87+i1738.7 + 732.1+i(-1644)+F3 = 0
1198 + i94.7+F3 = 0
F3 = -1198 - i94.7 = -1202 N.[4.52o]
Tan Ar = -94.7/-1198 = 0.07905
Ar = 4.52o = Reference angle.
A = 4.52 + 180 = 184.52o CCW = 85.5o W.
of S.(S85.5oW)