Two persons \( A \) and \( B \) running on a track in the same direction observe a car. \( A \) ...

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Two persons \( A \) and \( B \) running on a track in the same direction observe a car. \( A \) says that the car is moving in east direction and \( B \) says the car is moving in north direction. They contradict the direction but say that magnitude is same. If the speed of \( B \) is double that of the speed of \( A \), then the true direction of the car will be:
(1) \( \theta=\tan ^{-1}\left(\frac{1}{2}\right) \) North of East
(2) \( \theta=\tan ^{-1}\left(\frac{1}{2}\right) \) south of East
(3) \( \theta=\tan ^{-1} \) (2) North of East
(4) None of these
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