Posted by Mary on Saturday, April 20, 2013 at 4:50pm.
This has to do with vectors...I'm wondering if I set up the diagram correctly?
A plane has a speed of 250mph and flies with a bearing of N35degE. The wind is blowing from the west at 25 mph with a heading of due east. What is the actual speed and heading of the plane?
- Trig - Mary, Saturday, April 20, 2013 at 4:51pm
Whoops I forgot to include the diagram...here it is:
i.imgur [dot] com/RRY5pox.png
- Trig - Reiny, Saturday, April 20, 2013 at 10:02pm
I would tack on the wind vector to the end of the plane vector at the point P so the final end point is Q
Join Q to the origin O
vector OQ has our required direction and its magnitude represents the actual speed
By simple geometry angle P = 125░
so by the cosine law:
OP^2 = 250^2 + 25^2 - 2(250)(25)cos 125░
OP = 265.13
So the actual speed is 265.13 mph
Let the additional angle be ě
by the sine law:
sině/25 = sin 125/265.13
sině = .07724
ě = 4.43░
ě + 35░ = 39.43░
So the heading should be N 39.43░ E
- Trig - Mary, Sunday, April 21, 2013 at 12:29pm
Thank you <3 you are a lifesaver!
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