Question

In a harbour, wind is bowling at I
a spud of 72 km/hr of the flag
on the most of a boat ancher
anchord in the harbour flutter
along the north east direction
If the mous starts mouting at the
Shud of 51 km/hr to the North
What is the direction of the flag
on the most of the boat.​

Answer 1

a/c to question,

Velocity of wind ,  = 72 km/hr along N-E direction

or,

Velocity of boat ,  = 51 km/hr along North direction

To find out the direction of flag on the mast of the boat, we need to find out the relative velocity of wind w.r.t the boat.

Relative velocity of wind w.r.t the boat ,

= 72cos45\hat{i}+72sin45\hat{j}-51\hat{j}

=36\sqrt{2}\hat{i}+(36\sqrt{2}-51)\hat{j}

actually, angle between velocity of wind and velocity of boat is 135° [ see figure ]

Using parallelogram law of vectors, let  be the resultant vector making an angle β with

so,

= 51 × sin135°/(72 + 51cos45°)

= 1.0034

β = 45.099° ≈ 45.1° wrt N-E direction .

hence, the direction of flag on the mast of the boat is 0.1˚ w.r.t East.