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# 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.

Q. 4.14  In a harbour, wind is blowing at the speed of $\inline 72\; km/h$ 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  $\inline 51\; km/h$  to the north, what is the direction of the flag on the mast of the boat?

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According to the question the figure is shown below:-

The angle between velocity of wind and opposite of velocity of boat is (90 + 45)   =  135 degree.

Using geometry,

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

$\tan \beta \ =\ \frac{51}{50.8 }$

Thus                                                            $\beta \ =\ \tan^{-1} \frac{51}{50.8 }$

$=\ 45.11^{\circ}$

So the flag will be just 0.11 degree from the perfect east direction.

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