# Thread: Finding the actual velocity

1. ## Finding the actual velocity

An airplane flying at 500 km/h NW encounters a wind of 120 km/h blowing in the direction W25°S. Determine the actual velocity (ground velocity) of the plane.

Not sure If I got the right answer or not could someone look over it? https://imgur.com/a/RnzHt

Just in case you can't see my answer I wrote 394.51 km/h N32°W

2. ## Re: Finding the actual velocity

Air vector + wind vector = ground vector

Using the method of components ...

$A_x + W_x = G_x$

$500\cos(135)+120\cos(205)=G_x \approx -462.31$

$A_y + W_y = G_y$

$500\sin(135)+120\sin(205)=G_y \approx 302.84$

$|G| = \sqrt{G_x^2 + G_y^2} \approx 553 \, km/hr$

$\theta = 180+\arctan\left(\dfrac{G_y}{G_x}\right) \approx 147^\circ$ relative to the positive x-axis ...

$N \, 57^\circ \, W$ or $W \, 33^\circ \, N$, or (in real air navigation terns) on a track of $303^\circ$ relative to true North

3. ## Re: Finding the actual velocity

Thanks for the reply, but how are you finding the degrees 135 and 295 when only W25°S and NW are given?

4. ## Re: Finding the actual velocity

Originally Posted by Tyler010
Thanks for the reply, but how are you finding the degrees 135 and 295 when only W25°S and NW are given?
135 degrees and 205 degrees relative to the positive x-axis so that a calculator may be used to add the vector components

make a sketch of on a set of coordinate axes ...

5. ## Re: Finding the actual velocity

Ohhh, I drew mine like that but I thought the question had to say bearing in it so you could do it like that. An example question we were given it was solved like this, https://imgur.com/a/HAp3T the difference is that they give two degrees N60E and E20S.

Edit: Also, doesn't the bearing start clock-wise and not counter clockwise?

6. ## Re: Finding the actual velocity

The word “bearing” normally uses North as the starting axis with angle rotation in a clockwise direction.

N60E means to start on the North axis and rotate 60 degrees toward the East axis.

E20S means to start on the East axis and rotate 20 degrees toward the South axis.

In your initial problem, W25S means to start on the West axis and rotate 25 degrees toward the South axis.

All of these directions have to be converted to directions relative to the positive x-axis (East) in a counter-clockwise direction to conform to the reference used by a math scientific calculator.