# Airplane velocity with wind

## Homework Statement

A plane is travelling 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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## Homework Statement

A plane is travelling 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!

Simon Bridge
Homework Helper

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.

CWatters
Homework Helper
Gold Member
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).

Bandersnatch