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The Janasena Party President Pawan Kalyan has to start its procession in an area in Vijayawada where the wind is blowing at a speed of $ 20\,kmph $ along the north-east direction and party flags with the symbols of Hexagram (six-pointed star), on the vehicles are fluttering. If the procession starts with a speed of $ 14.14\,kmph $ towards north, find the direction fluttering of flags on the vehicles.
A) $ 37^\circ $ S of W
B) East
C) N-E
D) $ 53^\circ $ N of E

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Last updated date: 20th Jun 2024
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Answer
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Hint The velocity of wind has a direction and is a vector quantity. We need to take the net resultant vector due to the direction of the wind and the motion of the vehicles which will be the direction of the fluttering of the flags.

Complete step by step answer
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We’ve been given that the wind, when the procession starts, is flowing a speed of $ 20\,kmph $ along the north-east direction. And the party vehicles are moving with a speed of $ 14.14\,kmph $ towards the north direction.
When the vehicle is stationary, the flags will flutter in the northeast direction due to the wind. When the vehicle starts moving in the North direction, the flags will start moving in the South direction. Since there is also wind acting on the flag, we will have to take the addition of the two vectors.
So, taking the component of the wind in the North direction, it will be $ 20\cos 45^\circ = 20/\sqrt 2 $
Which will be equal to,
  $ \Rightarrow 20\cos 45^\circ = 14.14 $
This is exactly equal to the magnitude of the movement of the flag in the South direction due to the movement of the vehicle. So, the movement of the flag due to the movement of the vehicle cancels out the component of the wind in the North direction. So, the only remaining component of the flag will be due to the East component of the wind hence the flag will flow in the East direction.
So the correct answer will be option B.

Note
The flag moves southwards when the vehicles move northwards due to the flag experiencing wind in the South direction. Since the direction of the wind is in the North-East direction and the other direction of the wind due to the movement of the vehicles is in the south direction, we can expect the direction of flag fluttering to be between the North and the South direction towards the East direction so we can discard option (A).