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Question

In a harbour, the wind is blowing at the speed of 72km/h and flag on the mast of a boat anchors in the harbour flutter along the N-E direction. If the boat starts moving at 51km/h to the north, what is the direction of the flag on the mast of the boat?

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Solution

Velocity of the boat, Vb=51 km/h
Velocity of the wind, Vw=72 km/h
The flag is fluttering in the north – east direction. It shows that the wind is blowing toward the north – east direction. When the ship begins sailing toward the north, the flag will move along the direction of the relative velocity (Vwb) of the wind with respect to the boat.

The angle between vm and (vb)=90+45
tan β=51 sin(90+45)72+51 cos(90+45)
=51 sin 4572+51(cos 45)=51×127251×12
=5172251=5172×1.41451=5150.800
β=tan1(1.0038)=45.11
Angle with respect to the east direction =45.1145=0.11
Hence, the flag will flutter almost due east.

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