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Standard XII

Physics

Relative Velocity

A helicopter ...

Question

A helicopter is flying south with a speed of $50 k m h^{- 1}$ . A train is moving with the same speed towards east. The relative velocity of the helicopter as seen by the passengers in the train will be $50 \sqrt{2} k m h^{- 1}$ towards

northwest

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southwest

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northeast

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southeast

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Solution

The correct option is C southwest
$V_{H e l i c o p t e r, T r a i n} = V_{H e l i c o p t e r} - V_{T r a i n} = - 50^k - 50^i$ (Assume north as $+^k$ and east as $+^i$ )
Thus, direction is given as $t a n^{- 1} (\frac{- 50}{- 50})$ , thus it is $45^{o}$ with vertical in 3rd quadrant (x and y both negative), thus direction is Southwest.

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A helicopter is flying south with a speed of 50 kmh−1. A train is moving with the same speed towards east. The relative velocity of the helicopter as seen by the passengers in the train will be 50√2 kmh−1 towards

The correct option is C southwestVHelicopter,Train=VHelicopter−VTrain=−50^k−50^i (Assume north as +^k and east as +^i)Thus, direction is given as tan−1(−50−50), thus it is 45o with vertical in 3rd quadrant (x and y both negative), thus direction is Southwest.

A helicopter is flying south with a speed of $50 k m h^{- 1}$ . A train is moving with the same speed towards east. The relative velocity of the helicopter as seen by the passengers in the train will be $50 \sqrt{2} k m h^{- 1}$ towards