Calculating Airplane Velocity and Heading with Wind

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Homework Help Overview

The problem involves calculating the true velocity and heading of an airplane traveling at 350 km/h northeast while considering a wind blowing at 134 km/h south. Participants are tasked with determining the airplane's actual velocity and its velocity directly east.

Discussion Character

  • Exploratory, Assumption checking, Mixed

Approaches and Questions Raised

  • Participants discuss vector components and the implications of the terms "true velocity" and "ground track." Some express uncertainty about the wording of the problem and its clarity regarding the definitions of airspeed and ground speed.

Discussion Status

There is a mix of attempts to clarify the problem's wording and to validate calculations. Some participants have offered guidance on the interpretation of the question, while others have provided feedback on the correctness of the calculations presented.

Contextual Notes

Participants note potential ambiguities in the problem statement, particularly regarding the definitions of "true velocity" and whether the given speed refers to airspeed or ground speed.

joel amos
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Homework Statement


A plane is traveling at 350km/h northeast through a wind that is blowing 134km/h south.
a) What is its true velocity and heading?
b) What is its velocity directly east?

I'm really not sure how to set this up. I need some nice pointers or someone to solve it and explain how the got the answer. Thanks :)
 
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Adding vector components

Homework Statement


A plane is traveling at 350km/h northeast through a wind that is blowing 134km/h south.
a) What is its true velocity and heading?
b) What is its velocity directly east?

Homework Equations


Fx = F*cosƟ
Fy = F*sinƟ
Rx = Ax + Bx + Cx etc
Ry = Ay + By + Cy etc

The Attempt at a Solution


a) 272.27 km/h at 24.6 degrees north of east
b) 247.49 km/h

Am I correct? Can you please check my work? This is for a test!
 
You will have some course notes about this sort of problem, with worked examples.
Best practice is to start with those.

If that is the way the question is really worded, then it is very badly worded indeed. What does "true velocity" mean in this context? Havn't you just been given the plane's velocity? If that is not "true" then what is it?

Usually you are given the airspeed of the aircraft, and it's heading, and you have to work out the ground-speed and direction. Here it is not clear if 350kmph is the speed over the ground or what? The direction NE appears to be the direction of travel since part (a) asks for the heading (which direction the plane is pointing).

I think this needs to be cleared up.
 
I agree with Simon. Very missleading question.

I would assume that the use of the word "travelling" and the fact that the question asks for the heading means that "350km/h northeast" is referring to the ground track (the path over the ground).
 


Looks correct. Good job.
 

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