Relative Velocity of Aeroplane from A to B

[teng125]

An aeroplane starts from airport A to airport B, which is 600km away.
The course (N) over ground from A to B is 30°. The wind is blowing with
v(W) = 40 km/h from NW. The relative velocity is 200 km/h.

can somebody pls explain to me how does the vector diagram looks like??

i don't know what is course (N) and W

pls help

 

[berkeman]

N = North (drawn in the +y direction)
S = South (drawn in the -y direction)
E = East (drawn in the +x direction)
W = West (drawn in the -x direction)

Does that help? When it says the wind is from the NW (northwest), that means that the vector points down and to the right (aiming toward the southeast).


EDIT -- and the 30 degree thing is incomplete. It should say something like N 30 degrees E or something.

 

[teng125]

[The course (N) over ground from A to B is 30°.]

what does this mean??

 

[berkeman]

[The course (N) over ground from A to B is 30°.]

what does this mean??

I'm sorry, I have no idea. I've seen notation like North 30 degrees of East, which I believe would mean a vector that is rotated 30 degrees Northward, starting from East (but I'm not sure about that notation).

The only other thing I can think of is the absolute compass heading, which starts at zero degrees for North, and counts up clockwise:

N = 0 degrees

E = 90 degrees

S = 180 degrees

W = 270 degrees.

So an absolute heading of 30 degrees would be 1/3 of the way down from North, pointing to the east. Maybe that's what they mean. How in the world could they ask you that question without giving you a little information in your study materials about what they mean?


EDIT -- Kind of like this compass display from an airplane. Well, the numbers on it are shortened by 10 for ease of reading, but you get the idea.

http://en.wikipedia.org/wiki/Heading_indicator

 

[teng125]

the question is to ask to Draw the
vector diagram of velocities , which i cannot image how it looks like

 

[berkeman]

Start the drawing with the two cities (assuming my last interpretation of the question is correct). That puts city A at the origin, and city B at

(x,y) = (e,n) = (600cos(30 degrees),600sin(30 degrees))

That is the direction that you need the resultant ground-based velocity vector to point in, right? The ground-based velocity vector is the sum of the airspeed vector of the plane, plus the wind vector. The wind vector should be something like:

(Vx,Vy) = (Ve,Vn) = 40km/hr * (cos(45),-sin(45) (the wind is from the NorthWest, so it points down and right towards the southeast)

Now just work out the vector additions or subtractions...

I'm out for the day. Good luck!

 

[teng125]

thanx...