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Home » In a harbour, the 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?
In a harbour, the 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?
CBSE | Class 11 | Motion in a Plane | NCERT | Physics
In a harbour, the 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?

Answer –

According to the question, the velocity of the boat is 51 km/h and the velocity of the wind is 72 km/h.

The flag is flapping in the direction of northeast. It indicates that the wind is blowing from the north-east. When the ship starts sailing north, the flag will follow the direction of the wind’s relative velocity in relation to the boat.

According to the diagram, the angle between {{v}_{w}} and {{v}_{b}} is ( 90 + 45 ). So using the following expression, we get –

\tan \beta =\frac{51\sin (90+45)}{72+51\cos (90+45)}

here, \sin (90+45)=cos(90+45)=\frac{1}{\sqrt{2}}

\tan \beta =\frac{51}{50.800}

\beta ={{\tan }^{-1}}(1.0038)

\beta ={{45.11}^{\circ }}

Therefore, the angle with respect to the east direction = 45.11° – 45° = 0.11°

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