Physics question: a hammock is supported by two hooks at the same level...........?

a hammock is supported by two hooks at the same level. a man is seated in this hammock. at what angle relative to the horizontal will the tension in each suspending rope ( hence the pull on each hook) be equal to the mans weight?

Physics question: a hammock is supported by two hooks at the same level...........?
In a rope the force is acting in the direction of the rope.





For a given angle α to the horizontal you can separate the tension in an vertical and an horizontal part:


Fh = F·cos α


Fv = F·sin α





From a vertical force balance follows that the vertical part of the two suspending ropes must equal the weight of the man:


2 ·F·sin α = W





Moreover the magnitude of the tension in each rope should equal the weight of the man:


F = W





Hence:


2 ·W·sinα = W


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sinα = 1/2


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α = 30°



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