What am I overlooking? Vectors simple problem

[flyingpig]

Homework Statement

[PLAIN]http://img851.imageshack.us/img851/859/unledxnj.png

The Attempt at a Solution

ignoring all units for now, I took v = <1,-1> for plane

v + w_1 = <-2,0> and speed is 2

v + w_2 = <2,-4> and speed is √(20)

v + w_3 = <0,5> and speed is 5

v + w_4 = <11,1> and speed is√122

v + w_5 = <4,-3> and speed is 5

I thought it should be w_4 that increases the plane's speed the most and w_1 decreases the most, but it was wrong.

 

[SammyS]

Well, you do show (almost) that the question is not very well thought out.

The reason I say almost is that you should look at the change in speed, not just the final speed. The air speed you chose was √(2) .

But it is true that the plane's air speed is slow compared to the wind speed, as you have in your example, then the given answer answer is not correct.

Normally, I would expect the plane's air speed to be several times any wind speed.

What must the plane's air speed (the plane's speed w.r.t. the air) be, in order for the answers to be w₅ and/or w₃ respectively?

Furthermore, the above assumes that the air speed (actually the plane's velocity w.r.t. the air) is in the southeast direction. What if you assume that the plane's actual (resultant) velocity is in the southeast direction.

 

[Hammie]

My first observation: You do not know the speed of the plane. If you assign a vector <1,1> here, you may be saying that the plane is traveling at sqrt(2) ground speed.

adding the big vector, you can see you are actually reversing the direction of the plane.

I think a good assumption would be that this would be impossible. You might consider graphing all of the vectors and see which one might increase the speed the greatest and the one that might decrease the speed the greatest.

 

[flyingpig]

I am a bit confused, we are dealing with speed, so my change is still going to take the "biggest number" from my answers.

 

[flyingpig]

This problem is due soon and I am still out of ideas.

 

[flyingpig]

Sigh, i have the solutions

[PLAIN]http://img600.imageshack.us/img600/28/unledpb.png

 

[SammyS]

Interesting.

I would have to look a bit further at various examples before being convinced of the validity of that method of solution.

Added in Edit:

Well, I've pondered it some and, well ... I don't like it.

I'll try to take a little time out tomorrow and explain, but quickly, if |v| >> |w| then what the solution shows is approximately correct. But they actually use v = i - j & simply look at the component of w parallel to v. There is also a component of w perpendicular to i - j . They are not considering that effect at all.