Question

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

• A. ${tan}^{-1}\left(\frac{2}{7}\right)$
• B. ${tan}^{-1}\left(\frac{7}{2}\right)$
• C. ${tan}^{-1}\left(7\right)$
• D. ${tan}^{-1}\left(\frac{1}{7}\right)$

Answer 1

The correct option is D ${tan}^{-1}\left(\frac{1}{7}\right)$

Taking north as $\hat{j}$ , south as $-\hat{j}$

and east as $\hat{i}$ with west as $-\hat{i}$

so $V_A=80\left(\frac{\hat{j}+\hat{i}}{\sqrt{2}}\right)$

and $V_B=60\left(\frac{-\hat{j}+\hat{i}}{\sqrt{2}}\right)$

now $V_{AB}=V_A-V_B=10\sqrt{2}\hat{i}+70\sqrt{2}\hat{j}$

angle with north$\left(\hat{j}\right)$

will be $\theta =ta{n}^{-1}\frac{10\sqrt{2}}{70\sqrt{2}}=ta{n}^{-1}\frac{1}{7}$