A ship leaves the island of Guam and sails a distance 300 km at an angle 31.0 degrees north of west.? - vector sails
In which direction should now head for the resulting shift of 100 miles east of Guam? (Express your answer in a southeastern corner). I was most interested in how to solve this problem. I have the length of the vector displacement of 389, but can not calculate the angle.
Friday, January 15, 2010
Vector Sails A Ship Leaves The Island Of Guam And Sails A Distance 300 Km At An Angle 31.0 Degrees North Of West.?
2 comments:
I checked the value of the displacement vector necessary. Must of course be applied by the cosine formula to the triangle or retroactively. I did it ... 389.14 kilometers, and so agree with you.
He now has at least two ways:
(i) We could use the sine formula, in this triangle. If E is the most easterly point) (direction that gives
E 300/sin = 389.14 ... / Senior 31, e = asin (300 sin 31 / 389.14 ...) = 23.394 ... Degree
where the desired course to the south of east. Alternatively
(ii) from zero and an expression E Tan:
So, E = 300 sin 31 / [300 cos 31 + 100].
is that still E = 23.394 ... Degrees south of east.
Important note. These results are very informative. Get in on the plane geometry. However, because the earth is spherical, it will be errors in them a few tenths of a second to one percentage point. A better approach would be to spherical trigonometry, and problem drug use.
Long life and prosperity.
Breaking the resultant vector components.
First, we know that the component and the same as the component and the first route will be sailing, since y = 0 to the end and beginning.
Then
sin (31) * 300 = 154.5 kilometers
The x-component is the x component of the first sailing PLUS an additional 100 kilometers.
cos (31) * 300 +100 = 357.2 kilometers
The relationship between and with the components of x is equal to the tangent of the angle between them.
Therefore
Tan (angle) = 154.5km/357.2km
Tan (angle) = 0.4326
Angle = tan ^ -1 (0.4326)
= Angle of 23.4 degrees south of east.
Verify
sin (23.4) * 389 = 154.5
It is so that we know who controls and component output, and we have the right angle.
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