Answer
(a) The bird should head in a direction that is $23.6^{\circ}$ west of south.
(b) It would take 5.46 hours to cover a ground distance of 500 km.
Work Step by Step
(a) The wind is moving 40 km/h to the east. For the bird to fly directly south, the east-west component of the velocity of the bird relative to the air should be 40 km/h to the west.
We can find the angle $\theta$ west of south that the bird should head.
$sin(\theta) = \frac{40~km/h}{100~km/h}$
$\theta = sin^{-1}(\frac{40}{100}) = 23.6^{\circ}$
The bird should head in a direction that is $23.6^{\circ}$ west of south.
(b) We can find the component of the bird's velocity directed to the south.
$v_{south} = (100~km/h)~cos(23.6^{\circ})$
$v_{south} = 91.6~km/h$
$t = \frac{500~km}{91.6~km/h} = 5.46~hours$
It would take 5.46 hours to cover a ground distance of 500 km.
