1. ## vectors

An airplane is flying due north at 440 miles per hour. A wind begins to blow in the direction South 45 degrees East (S45E) at 59 miles per hour. Find the bearing the pilot must fly the aircraft to continue traveling due north.

The correct answer is North 11.8 degrees West or N11.8W. I'm not sure how they got that answer. I'd really appreciate some help...ASAP!!!!!!!!! PLEASE. THANKS!

2. Originally Posted by iheartthemusic29
An airplane is flying due north at 440 miles per hour. A wind begins to blow in the direction South 45 degrees East (S45E) at 59 miles per hour. Find the bearing the pilot must fly the aircraft to continue traveling due north.

The correct answer is North 11.8 degrees West or N11.8W. I'm not sure how they got that answer. I'd really appreciate some help...ASAP!!!!!!!!! PLEASE. THANKS!
1. Draw a sketch.

2. The flight of the airplane is described by $\vec a= \left(\begin{array}{c}0\\440 \end{array}\right)$ and the wind can be described by $\vec w= \left(\begin{array}{c}\frac{59}2 \sqrt{2}\\ -\frac{59}2 \sqrt{2} \end{array}\right)$

3. Therefore the course over ground (cog) is $\vec c = \vec a + \vec w$ . That means:

$\vec c = \left(\begin{array}{c}\frac{59}2 \sqrt{2}\\ 440-\frac{59}2 \sqrt{2} \end{array}\right)$

4. To calculate $\alpha$ use the tan-function:

$\tan(\alpha) = \frac{\frac{59}2 \sqrt{2}}{440-\frac{59}2 \sqrt{2}}~\implies~ \alpha \approx 5.9798...^\circ$

5. I've no idea where the given result comes from What I mean: The pilot is steering N, the airplane is flying N5.98°E so it must be sufficient if the pilot steers to N5.98°W ...?