To a person going east in a car at velocity of 25 kmph, a train appears to move towards north with a velocity of $25 \sqrt{3} k m p h$ . The actual velocity train is

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25 kmph, $30 °$ S of E

50 kmph, $30 °$ S of W

50 kmph, $60 °$ N of E

25 kmph, $60 °$ N of E

answer is D.

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Detailed Solution

${\bar{V}}_{T m} = {\bar{V}}_{T} - {\bar{V}}_{m}$ , ${\bar{V}}_{T} = {\bar{V}}_{T m} + {\bar{V}}_{m}$ , $| {\bar{V}}_{T} | = \sqrt{{\bar{V}}_{T m}^{2} + {\bar{V}}_{m}^{2}} = 50 k m p h$

$\tan θ = \frac{V_{T m}}{V_{m}} = \frac{25 \sqrt{3}}{25}$ , $∴ θ = 60^{0}$ N of E

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