Answer
The direction of the boat's velocity relative to the ground is $16.1^{\circ}$ west of north.
Work Step by Step
We can find the components of the boat's velocity relative to the ground:
$v_x = (8.0~m/s)~sin~30^{\circ}-2.0~m/s = 2.0~m/s~(west)$
$v_y = (8.0~m/s)~cos~30^{\circ} = 6.93~m/s~(north)$
We can find the direction of the boat's velocity relative to the ground as an angle $\theta$ that is west of north:
$\tan~\theta = \frac{2.0~m/s}{6.93~m/s}$
$\theta = tan^{-1}~(\frac{2.0~m/s}{6.93~m/s})$
$\theta = 16.1^{\circ}$
The direction of the boat's velocity relative to the ground is $16.1^{\circ}$ west of north.
