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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 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?

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According to the question the figure is shown below:-  

                                           Chapter - 4     ,       20156

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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