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?
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 vw and (–vb) = 90° + 45°
tan β = 51sin (90+45) / 72 + 51cos(90+45)
∴ β = tan-1 (1.0038) = 45.11°
Angle with respect to the east direction = 45.11° – 45° = 0.11°
Hence, the flag will flutter almost due east.
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