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

$\left|\stackrel{\rightharpoonup }{\hspace{0.17em}{V}_W}\right|$=speed of wind = 72 km/hr.
$\left|\stackrel{\rightharpoonup }{V_b}\right|=$speed of boat = 51 km/hr.
$\left|\stackrel{\rightharpoonup }{V_w}\right|$=velocity of wind along N--E direction

=$\left(72\cos {45}^0\right)\hat{i}+\left(72 \sin {45}^0\right)\hat{j} km/hr$
 

velocity of boat = ${\stackrel{\rightharpoonup }{v}}_b=velocity of boat=51\hat{j}$km/hr

${\stackrel{\rightharpoonup }{v_{ }}}_{w/b}=$velocity of wind relative to the boat=$-{\stackrel{\rightharpoonup }{v}}_b+{\stackrel{\rightharpoonup }{v}}_w$

    =$\left(-51\hat{j}+36\sqrt{2}\hat{i}+36\sqrt{2} \hat{j}\right)km/hr$

    =$36\sqrt{2}\hat{i} km/hr$

The flag will flutter due east.