three people are trying to hold a lion still for the vet. The lion, in the center, is wearing a collar with three ropes attached to it and each person has a hold of the rope. charlie is pulling in the direction of 62 degrees west of north with a force of 175 newtons. Sam is pulling in the direction of 43 degrees east of north with a force of 200 newtons. What is the direction and magnitude of the force which must be exerted by Alice on the third rope to counterbalance Sam and Charlie?

Question

Henry · Answer

Charlie: 175 N. @ 152 Deg.,CCW.
Sam: 200 N. @ 47 Deg.,CCW.

X = 175*cos152 + 200*cos47 = -18.1 N.
Y = 175*sin152 + 200*sin47 = 228.4 N.

Alice: Force must be equal and opposite
The vector sum of Charlie and Sam's force.

X = 18.1 N.
Y = -228.4 N.

tanA = Y/X = -228.4 / 18.1 = -12.61878.
A = -85.5 Deg. = 85.5 Deg S of E
A = -85.5 + 360 = 274.5 Deg.,CCW..

M = X / cosA = 18.1 / cos274,5 = 230.7 N.@ 274.5 Deg.