In a harbour , wind is blowing at the speed of `27 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 ?

Explanation

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 of relative 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 sin 135 ^(@))/(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 .