Vectors help please!

casherr

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This question has me really stuck because I can't seem to figure out how the diagram would look. Any help would be greatly appreciated!

A pilot wishes to fly her plane from Vectortown to Primeville, 850km away in the direction [N55W]. Her plane can fly 310km/h in still air, and the wind is measured coming from the northeast. The speed of the wind is 201km/h. In which direction should the pilot head the plane?
 

Subhotosh Khan

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This question has me really stuck because I can't seem to figure out how the diagram would look. Any help would be greatly appreciated!

A pilot wishes to fly her plane from Vectortown to Primeville, 850km away in the direction [N55W]. Her plane can fly 310km/h in still air, and the wind is measured coming from the northeast. The speed of the wind is 201km/h. In which direction should the pilot head the plane?
Can you draw 'x'(East) and 'y'(North) axes (with arbitrary origin) and relative positions of Vectortown(V) and Primeville(P)? Now draw a vector VP. This your desired displacement vector. What is the unit vector along VP (displacement)?

What does the wind-vector look like? What is the unit vector wind-flow?

If you are still stuck, reply back showing your sketch and other associated work. Tell us exactly where you are stuck now?
 

casherr

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IMG_0602.jpglike this? next do i need to make a resultant vector connecting the wind and VP vector?
 

Subhotosh Khan

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View attachment 26556like this? next do i need to make a resultant vector connecting the wind and VP vector?
Correct - that will give the vector of the velocity of the plane. Carefully consider the directions of the vectors

You have to calculate:

In which direction should the pilot head the plane?

For that, you need work with the unit vectors.

What is the unit vector along VP (displacement)?

What is the unit vector wind-flow?
 

casherr

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IMG_0623.jpgthis is what I worked out. also, there was a typo in my original question, the speed of the wind is 210km/h.
 

nasi112

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I would choose vector \(\displaystyle \vec{VP}\) to be \(\displaystyle 310 \ km/h\)
 

lex

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casherr

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lex

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But lex, how can that be true? Moving against the wind with still air speed?
I'm not sure I understand your question. The wind has two effects on the plane - it blows it off its heading and it changes its speed.
The plane will not end up going 310km/hr, if that is what the issue is.
(If there had been no wind i.e. if there was "still air", the plane would aim directly for the destination and would travel at 310km/hr. As it is the plane has to head towards the wind and be blown into the correct direction for its destination, and, as I think you are pointing out, it will not achieve 310km/hr in the direction of its destination. Its speed will be reduced).
 

skeeter

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But lex, how can that be true? Moving against the wind with still air speed?
The airspeed is not "still" ... airspeed is how fast the plane moves in the air mass, while wind is how fast the airmass moves relative to the Earth. The vector sum of the airspeed vector and the wind vector is the track vector ... the resultant vector with which the plane moves with respect to the ground.
 

nasi112

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did i do something wrong?
I think you did correctly. I had some misunderstanding, but lex and skeeter explained it well.



I'm not sure I understand your question. The wind has two effects on the plane - it blows it off its heading and it changes its speed.
The plane will not end up going 310km/hr, if that is what the issue is.
(If there had been no wind i.e. if there was "still air", the plane would aim directly for the destination and would travel at 310km/hr. As it is the plane has to head towards the wind and be blown into the correct direction for its destination, and, as I think you are pointing out, it will not achieve 310km/hr in the direction of its destination. Its speed will be reduced).
Ok, now it makes sense. The speed will be reduced and the direction will be changed. I have cleared the misunderstanding.



The airspeed is not "still" ... airspeed is how fast the plane moves in the air mass, while wind is how fast the airmass moves relative to the Earth. The vector sum of the airspeed vector and the wind vector is the track vector ... the resultant vector with which the plane moves with respect to the ground.
Nice explanation skeeter. Sum of wind speed and still air speed vectors would give us the speed of where the pilot will be heading (N55W).
 
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lex

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Yes. Skeeter's explanation is very informative; clear and to the point.
 
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