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Q.

A person is travelling in a train moving due south with velocity 80 kmph and his friend Q is travelling in a car moving due west with velocity 60 kmph. Q finds that his friend P is travelling with velocity

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a

200 kmph \tan^{- 1} (4/3) NE

b

100 kmph \tan^{- 1} (4/3) S of E

c

100 kmph S of E

d

100 kmph \tan^{- 1} (4/3) E of S

answer is D.

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Detailed Solution

Question Image

$\vec{V_{P}} = - 80 \hat{j}$

$\overset{⇀}{V_{Q}} = - 60 \hat{i}$

$\vec{V_{P Q}} = {\bar{V}}_{P} - {\bar{V}}_{Q}$

$= - 80 \hat{j} + 60 \hat{i} - 60 \hat{i} - 80 \hat{j}$

$| V_{PQ} | = \sqrt{60^{2} + 80^{2}}$

$= \sqrt{3600 + 6400}$

$= \sqrt{10000}$

$= 100 kmph$

$Tan θ = \frac{80}{60} = \frac{4}{3}$

$θ = \tan^{- 1} (\frac{4}{3}) S of E$

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A person is travelling in a train moving due south with velocity 80 kmph and his friend Q is travelling in a car moving due west with velocity 60 kmph. Q finds that his friend P is travelling with velocity