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A car A is going north east at 80 $k m h^{- 1}$ and another car B is going south east with a velocity of 60 $k m h^{- 1}$ . The velocity of A relative to B makes an angle with the north equal to

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a

$\tan^{- 1} (\frac{1}{7})$

b

$\tan^{- 1} (7)$

c

$\tan^{- 1} (\frac{2}{7})$

d

$\tan^{- 1} (\frac{7}{2})$

answer is D.

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Detailed Solution

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${\vec{V}}_{A} = 40 \sqrt{2} \overset{\land}{i} + 40 \sqrt{2} \overset{\land}{j}, {\vec{V}}_{B} = 30 \sqrt{2} \overset{\land}{i} - 30 \sqrt{2} \overset{\land}{j} {\vec{V}}_{A B} = {\vec{V}}_{A} - {\vec{V}}_{- B} = 10 \sqrt{2} \overset{\land}{i} + 70 \sqrt{2} \overset{\land}{j} \tan θ = \frac{10 \sqrt{2}}{70 \sqrt{2}} = \frac{1}{7} w i t h N o r t h$

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A car A is going north east at 80kmh–1and another car B is going south east with a velocity of 60 kmh–1. The velocity of A relative to B makes an angle with the north equal to