Q 11-03-026NEETJEE MainEasy
Car A moves east at $30$ m/s and car B moves north at $40$ m/s. The velocity of B relative to A is
Answer: (C) $50$ m/s at $\tan^{-1}\left(\dfrac{4}{3}\right)$ north of west
$$\vec{v}_{BA} = \vec{v}_B - \vec{v}_A = 40\,\hat{N} - 30\,\hat{E} = 40\,\hat{N} + 30\,\hat{W}$$
Magnitude $= 50$ m/s. It points between north and west, making $\tan^{-1}\left(\dfrac{40}{30}\right) = \tan^{-1}\left(\dfrac{4}{3}\right)$ with the west direction, i.e. north of west.
Solution by Sreeraj P, M.Sc Physics