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?

Question

anonymous · Answer

The answer should be 0.1 degreee   wrt to east direction

anonymous · Answer

Oops I got my diagram wrong. Anyhow,
The velocity of the wind it towards N-E. The boats travels in the North direction.Since the new velocity of the flag will be the relative velocity of the wind with respect to the boat.Let x be the angle between the wind velocity and the new relative velocity of the flag.

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x= arctan ( 51 sin(135))/(72+ 51 cos135)) = arctan(51/72 sqrt 2 - 51) = arctan(1.0038) = 45.1086 degrees.
=> the flag makes 0.1086 degrees with west.