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
Concept. $\vec v_{BA} = \vec v_B - \vec v_A$.
Step 1. Vector. $40\hat N - 30\hat E = 40\hat N + 30\hat W$, magnitude $50$ m/s.
Step 2. Direction. Between north and west, at $\tan^{-1}\left(\dfrac{40}{30}\right) = \tan^{-1}\left(\dfrac43\right)$ from west.
Answer. $50$ m/s at $\tan^{-1}\left(\dfrac43\right)$ north of west (Option C).
Solution by Sreeraj P, M.Sc Physics