__Question 4.14__:

In a harbor, wind is blowing at the speed of 72 km/h and the flag on the mast of a boat anchored in the harbor 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 ?

__Solution__:

Velocity of the boat,

*v*

_{b}= 51 km/h

Velocity of the wind,

*v*

_{w}= 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 (

*v*

_{wb}) of the wind with respect to the boat.

The angle between

*v*

_{w}and (–

*v*

_{b}) = 90° + 45°

tan β = 51 Sin (90 + 45) / (72 + 51 Cos (90 + 45)

Substituting and solving we get,

tan β = 51 / 50.80 = 1.0038

∴ β = tan

^{-1}(1.0038) = 45.11

^{0}

Angle with respect to the east direction = 45.11° – 45° = 0.11°

Hence, the flag will flutter almost due east.

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