Find unknown wind velocity given airlplane's speed

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Homework Help Overview

The discussion revolves around determining the unknown wind velocity affecting an airplane's flight path. The problem involves vector analysis, specifically how the airplane's airspeed and the wind's influence result in a different observed ground speed.

Discussion Character

  • Exploratory, Assumption checking, Problem interpretation

Approaches and Questions Raised

  • Participants are examining the relationship between the airplane's airspeed and the observed ground speed, questioning how both vectors can point east while resulting in a westward outcome. There is a focus on identifying which vectors combine to produce the resultant vector.

Discussion Status

The discussion is active, with participants exploring the implications of vector directions and the observer's perspective. Some guidance has been offered regarding the interpretation of the vectors and their effects on the airplane's trajectory.

Contextual Notes

There is some confusion regarding the directionality of the vectors involved, particularly how the wind's direction can lead to an observed motion that seems counterintuitive. The problem is framed within the constraints of a homework assignment, which may limit the information available for discussion.

Gardunf070
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Homework Statement
An aeroplane flies with an airspeed of 50.0 m/s [E40°N]. If the velocity of the plane, according to an observer on the ground, is 30.0 m/s [S45°E], what is the wind velocity?
Relevant Equations
Here is the answer:
The wind velocity is 56 m/s [W72°S]
But I don't understand how is that it ends up on the west side if both vectors were pointing east.
 
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:welcome:

So what is  your answer for the wind speed?
 
Gardunf070 said:
Homework Statement: An aeroplane flies with an airspeed of 50.0 m/s [E40°N]. If the velocity of the plane, according to an observer on the ground, is 30.0 m/s [S45°E], what is the wind velocity?
Relevant Equations: Here is the answer:
The wind velocity is 56 m/s [W72°S]

But I don't understand how is that it ends up on the west side if both vectors were pointing east.
Which two vectors add to make the third?
 
Gardunf070 said:
Here is the answer:
The wind velocity is 56 m/s [W72°S]

But I don't understand how is that it ends up on the west side if both vectors were pointing east.
Welcome, @Gardunf070 !

What do you believe ends up on the West side?

W72°S is only the direction towards which the wind is blowing.
The observer on the ground feels that the wind is moving from the NE to the SW quadrant.

Not being able to see the ground as a reference, but only his instruments, the pilot believes that the airplane is moving from the SW to the NE quadrant at 50 m/s.

Simultaneously, that observer on the ground believes that the plane is moving from the NW to the SE quadrant at 30.0 m/s, although strangely, its nose points approximately towards the NE (the airplane is "crabbing").

1Ckx87.gif
 
Last edited:

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