When the boat is anchored in the harbour, the flag flutters along the N-E direction. It shows that the velocity of wind is along the north-east direction. When the boat starts moving, the flag will flutter along the direction of relative velocity of wind w.r.t. boat. Let

→

v

wb be the relative velocity of wind w.r.t. boat and β be the angle between

→

v

wb and

→

v

w. Refer Fig.
Now,

→

v

wb=

→

v

w+(−

→

v

b)
Here, |

→

v

w|=72kmh−1
|−

→

v

b|=51kmh−1
Angle between

→

v

w and −

→

v

b is 135° i.e. θ=135°.
Then
tan‌β=

51‌sin‌135°

72+51‌cos‌135°

=

51‌sin‌45°

72+51(−cos‌45°)

=

51× 1 √2

72−51( 1 √2 )

=1.0039
∴β=tan–1(1.0039)=45.1°
Angle w.r.t. east direction =45.1°−45°=0.1°
It means the flag will flutter almost due east.