Question

# A political party has to start its procession in an area where wind is blowing at a speed of 41.4 km/h and party flags on the vehicles are fluttering along north-east direction. If the procession starts with a speed of 40 km/h towards north, find the direction of flags on the vehicles.

A

south of east

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B

north of east

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C

south of east

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D

north of east

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Solution

## The correct option is C south of east When the procession is stationary, the flags flutters along the north - east direction.It means wind is flowing along the north-east direction.The flags will start fluttering along the direction of relative velocity of wind w.r.t.procession.As soon as procession gets into motion As the car will move along north with velocity vp,the flags will flutter in the resultant direction of wind. We can say the flag will flutter along →vWP,relative velocity of wind w.r.t the procession. →vWP=→vW+(−→vP) →vP=40^j →vW=41.4cos45^i+41.4sin45^j →vW=41.4√2^i+41.4√2^j →vWP=→vW−→vP = 41.4√2^i+41.4^j√2−40^j →vWP=41.4√2^i+(41.4√2−40)^j tanθ=(vyvx)=(41.4√2−40)(41.4√2) tanθ≈−13 θ=tan−1(−13) Where θ is the angle made south of east direction.

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