Precalculus Vector Help
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Precalculus Vector Help

[From: ] [author: ] [Date: 12-01-07] [Hit: ]
We can thus assume that the towlines also have equal magnitudes. Write the resultant tension T of each towline as a function of θ.Please help, I dont know what to do when not given the angle Thank you!-You need to write an equation for T in terms of θ.So you are not giving a numerical answer.......
The Question:
A loaded barge is being pulled by two tugboats and the magnitude of the resultant is 6000 pounds directed along the axis of the barge. The tugboats (one on either side of the barge) have towlines that both make angles of θ with the axis of the barge. We can thus assume that the towlines also have equal magnitudes. Write the resultant tension T of each towline as a function of θ.

Please help, I don't know what to do when not given the angle Thank you!

-
You need to write an equation for T in terms of θ. So you are not giving a numerical answer. Sum the forces along the axis of the barge:

ΣF = 6000
Tcosθ + Tcosθ = 6000
2Tcosθ = 6000
T = 3000/cosθ

or

T = 3000secθ
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