1. ## Vector problem

Q: an airplane is flying at an airspeed of 600 km/hr in a cross-wind that is 30 degrees west of north at a speed of 50 km/hr. In what direction should the plane fly to end up going due west?

Its been years since I did this, but am having a test and this problem will show up on it

2. Originally Posted by highc1157
Q: an airplane is flying at an airspeed of 600 km/hr in a cross-wind that is 30 degrees west of north at a speed of 50 km/hr. In what direction should the plane fly to end up going due west?
air vector + wind vector = ground vector

let $\displaystyle \theta$ = angle relative to due West for the Air vector

using the method of components ...

$\displaystyle A_x + W_x = G_x$

$\displaystyle 600\cos{\theta} + 50\cos(60) = G$

$\displaystyle A_y + W_y = G_y$

$\displaystyle 600\sin{\theta} + 50\sin(60) = 0$

solve for $\displaystyle \theta$ using the 2nd equation. If you need to find the groundspeed, $\displaystyle G$, use the value found for $\displaystyle \theta$ and the 1st equation.