Can someone solve a word problem determining force placed on a barge

[From: ] [author: ] [Date: 12-04-19] [Hit: ]

I might be tempted to use navigational directions which are measured from North, going eastward (North = 0, East = 90, South = 180, etc.)In that case,......

D = 30.36 degrees (= approx. 0.53 pi)

Becasue of the wording of the question, this is the angle you must get.

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Because this problem involves a barge, I might be tempted to use navigational directions which are measured from North, going eastward (North = 0, East = 90, South = 180, etc.)
In that case, the North component is a function of the cosine and the East component is a function of the sine.
The pythagorean theorem works the same way, and the direction uses
Tan = opposite/adjacent = East/North

You would have gotten a direction of 59.64
which is OK since N 59.64 E (as expressed in old navigation jargon)
is the same direction as E 30.36 N.

You should make a drawing as you go through these problems (even if the drawing is not to scale).

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Mathematicians calculate angles from the x-axis (East) and go counterclockwise.
Navigators calculate directions from North (y-axis) and go clockwise.
The direction they get is called an Azimuth by navigators (or a course, if it is a line followed by the ship)
Navigators do have a name for the angle as calculated by mathematicians: it is called the Amplitude, but in modern navigation, it is only used for calculations involving sunrise and sunset.

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-Separate your forces into vector components in the East and North directions.
-Northeast means an angle of 45°, so the East component of that force will be 200*cos(45), and the North component will be the same but using sin()
-Add the similar components together to get the resultant force in terms of East and North forces.
-Use those forces as legs in a right triangle with the Pythagorean Theorem to find the magnitude of the resultant force
-To find the resultant angle, note that the tangent function of the resultant angle is equal to the resultant North force divided by the resultant East force... tan(theta) = North/East
-The first rope is horizontal (angle = 0), so no extra work needs to be done, theta is your answer.

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