Vector word problem (finding angle away from resultant vector)
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Vector word problem (finding angle away from resultant vector)

[From: ] [author: ] [Date: 11-09-08] [Hit: ]
............
The thrust of an airplane's engines produces a speed of 361 mph in still air. The wind velocity is given by (42, -7). In what direction should the airplane head to fly due south? Give your answer as an angle from due south rounded to three significant digits.

I tried drawing a rectangle with sides of 361 and 7√37 (I got this by doing √(42² + (-7)²) )
solving for the hypotenuse, I did √(361² + (7√37)²) = 363.5024
and then i did cos(theta) = adjacent /hypotenuse = 361/363.5024
with cos = 6.73
but this answer was counted as wrong :/
What am I doing wrong?
Thanks :]

-
OK so you want a picture something like this:

.....A
......
......
......
......
......
B...C
.....D

A, C and D are all meant to be on a straight vertical line. AB is the plane engine velocity vector (length 361) and BD is the wind vector (42, -7), which I assume means +42 in the x (east) direction and -7 in the y (south) direction, as I've drawn it there. AD is the final velocity vector, which needs to be due south. C is the point due east of B on the AD line, so there are right angles at C.

If CAB is the angle at A, then sin(CAB) = BC / AB = 42 / 361
=> CAB = 6.68 degrees

Interestingly the wind north/south component (the -7) doesn't affect the answer at all. All we need is the x (east-west) component of the wind to cancel out the x (east-west) component of the plane engine velocity.

I think your method was wrong because you can't assume that the wind speed is perpendicular to the plane speed vector, so you can't add them using pythagoras' theorem.
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