1. ## Vector Problem

Hey guys:
An airplane is flying at an airspeed of 500 km/hr in a wind blowing at 60 km/hr toward the southeast. In what direction should the plane head to end up going due east? What is the airplane's speed relative to the ground?

Thanks,
Peter

2. Originally Posted by flybynight
Hey guys:
An airplane is flying at an airspeed of 500 km/hr in a wind blowing at 60 km/hr toward the southeast. In what direction should the plane head to end up going due east? What is the airplane's speed relative to the ground?
did you make a sketch?

air vector + wind vector = ground vector

using the method of components ...

$\displaystyle A_x + W_x = G_x$

$\displaystyle 500\cos{\theta} + 60\cos(-45) = G\cos(0)$

$\displaystyle A_y + W_y = G_y$

$\displaystyle 500\sin{\theta} + 60\sin(-45) = 0$

finish it ... solve for $\displaystyle G$ and $\displaystyle \theta$

3. So then Theta=4.86756 degrees and G=540.623?

4. Originally Posted by flybynight
So then Theta=4.86756 degrees and G=540.623?
close enough ... $\displaystyle \theta$ is degrees North of East and G is in km/hr