Answer
(a) The plane should head in a direction that is $14.5^{\circ}$ north of west.
(b) The speed of the plane over the ground is 309.8 km/h, and the plane is heading due west.
Work Step by Step
(a) The wind is moving 80.0 km/h to the south. For the plane to fly due west, the north-south component of the velocity of the plane relative to the air should be 80.0 km/h to the north.
We can find the angle $\theta$ north of west that the plane should head.
$sin(\theta) = \frac{80.0~km/h}{320.0~km/h}$
$\theta = sin^{-1}(\frac{80.0}{320.0}) = 14.5^{\circ}$
The plane should head in a direction that is $14.5^{\circ}$ north of west.
(b) We can find the component of the plane's velocity directed to the west.
$v_{west} = (320.0~km/h)~cos(14.5^{\circ})$
$v_{west} = 309.8~km/h$
The speed of the plane over the ground is 309.8 km/h, and the plane is heading due west.
