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Three men are pulling on a tree attached with ropes to keep it from falling down. If one man is pulling the rope with a force of 370N acting at 30 degrees east of north and the second man is pulling with a force of 280N acting at 70 degrees west of south. What force should the third man pull with and in what direction? PLEASE HELP AND EXPLAIN THANK YOU SO MUCH

Answer :

Hagrid
The correct answer to this question is 48.8N on a bearing of 134.2 degrees.

In order to solve this, first we need to find the resultant force of the men pulling in the north and south directions:

F = 40 - 6 = 34N [due south - 180]

Then, find the resultant force.

R^2 =34^2 + 35^2 
R^2 = 2381
R = sqrt(2381)
R = 44.8N

The angle from the vertical is given by:
tan(x) = 35/34
tan(x) = 1.0294
angle = 45.8 degrees

Taking N as zero degrees, then it bears 134.2 degrees.

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