In a harbor, wind is blowing at the speed of 72 km/h and the flag on the mast of a boat anchored in the harbor flutters along the N-E direction. If the boat starts moving at as speed of 51 km/h to the north, what is the direction of the flag on the mast of the boat ?

The flag is fluttering in the north-east direction. It shows that the wind is blowing toward the north-east direction. When the ship begins sailing toward the north, the flag will move along the direction of the relative velocity ($v_{wb}$) of the wind with respect to the boat.

The angle between $v_w$ and $v_b$ $=90+45$

$tan\theta =\frac{51sin(90+45)}{(72+51cos(90+45)}$

Substituting and solving we get,

$tan\theta =\frac{51}{50.80}=1.0038$

$\theta ={tan}^{-1}\left(1.0038\right)={45.11}^0$

Angle with respect to the east direction = $45.11-45=0.11$

Hence, the flag will flutter almost due east.