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posted by  Eshia on 11/1/2009 7:04:39 PM  |  status: Live  |  Earned Karma: 35

Not a solution just direction

Course Textbook Chapter Problem Needs by
Calculus Based Physics Physics for Scientists and Engineers with Modern Physics (4th) by Giancoli 3 71P 11/30/2009 at 12:00:00 PM
Question Details:
An airplane whose, airspeed is 580 km/h is supposed to fly in a straight pat 38.0 degrees N of E. But a steady 72 km/h wind is blowing from the North. In what direction should the plane head?
I have drawn a diagram that I think is good but I can't get it on here, any advise on that?
Then I found my X and Y components:
vpg= vpg cos(θ)
vpa =vpa cos(θ)
vag = 0
vpg= vpg sin(θ)
vpa =vpa sin(θ)
vag = vagsin(θ)
using the theorem of pythagoras I found what I hope to be Vpa.
vpa = √(vpg)2 + (vpa)2 = 575.51 km/h
Now for the tricky part, I know that in order for the plane to go where it needs to that it should compensate for the wind by heading a bit further north and a bit further south.
I am not sure of how to get to that part. This is an odd numbered problem so the answer is in my book, however I am really conflicted as to what to do next when I try to solve for the angles i get 38 for both cosine angles. I think this means I was doing something very wrong. If I could get help with what I should be doing next that would be great. I need to fully understand this concept if I am ever to accomplish this on my own. Get me close guys but don't give it away.
Eshia
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Oracle
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posted by Physics-Ga on 11/1/2009 10:03:59 PM  |  status: Live
Asker's Rating: Helpful   
Response Details:
The diagram editor hung up on me, but I will try to explain.
Let A be the vector velocity of the plane (we need to find this)
B = the vector velocity of the wind.
Then A + B = C   where C is the velocity of the plane in the wind.
We know B (direction) and C and need to find the direction of A (and magnitude of C).
Ax + Bx = Cx
Ay + By = Cy
A cos θ = C cos 38      the x-components
A sin θ - 72 = C sin 38    the y-components
Now, I think that if you square these equations and add them you can
use simple trigonometric identities to solve 
You may need to also use the identity  A2 + B2 - 2 A B cos φ = C2   where φ = 90 - θ
To do this write A - (-B) = C   where you are subtracting the vector -B from A
(draw a diagram to see this putting A and -B  tail-to-tail and C is the vector that closes the triangle
90 - θ = φ is then the angle between  A and -B)
Can't guarantee but looks solvable.
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Karma Points: 35
posted by Eshia on 11/5/2009 12:29:50 AM  |  status: Live
Asker's Rating: N/A-Posted by Person Asking Question   
Response Details:
I broke down and used the law of sines on this one it was just easier, I suppose there is no need to be impressive about my answer as long as I have an approach that works.
Eshia
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