In a harbour, wind is blowing at the speed of 72 km/h and a 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? from Physics Motion in A Plane Class 11 Manipur Board
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In a harbour, wind is blowing at the speed of 72 km/h and a 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?

Let east be taken along X-axis and north along Y-axis.

 

Velocity of wind is,

 stack straight v subscript straight w with rightwards arrow on top space equals space 72 space km divided by hr space along space NE space direction

     equals 72 space cos space 45 degree space straight i with hat on top space plus space 72 space sin space 45 degree space straight j with hat on top

     equals 50.9 straight i with hat on top space plus space 50.9 straight j with hat on top

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                              equals 51 straight j with hat on top

The flag flutters in the direction of relative velocity of wind relative to boat.

The relative velocity of wind w.r.t. the boat is,

straight v with rightwards arrow on top subscript wb equals straight v with rightwards arrow on top subscript straight w minus straight v with rightwards arrow on top subscript straight b equals 50.9 straight i with hat on top minus 0.1 straight j with hat on top

Since Y component of velocity is approximately zero, hence the flag will flutter almost due east.
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