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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

1 Answer

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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.