In a harbour ,wind is blowing at the speed of 27 km //hand 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 ?

In a harbour ,wind is blowing at the speed of 27 km //hand the flag on

1.	In a harbour ,wind is blowing at the speed of 27 km //hand 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 ?
Answer» Solution :As the flag FLUTTERS in the N-E direction , the wind must be flowing in the N-E direction. When the boat start moving , the flag will flutter in the direction ofrelative velocity of wind w.r.t. boat . `\|vecv_(w)\|=72 km //h` `\|vecv_(b)\|=51 km//h` If `beta` is the angle between `vec v_(w) and -vecv_(b)` `tan beta =(51 sin135 ^(@))/(72+51 cos 130^(@))` `=((51xx1 sqrt2))/(72-51xx1sqrt2)` `=131.1//51.1=0.9965` `therefore beta=tan^(-1) (1.0038)=45.1^(@)`(with S-E) `therefore` Angle with respect to direction of east `=45.1-45^(@)=0.1` (with east) Hence , the direction of the flag is almost towards east .