Question

Two persons A and B running on a straight track in the same direction observe a car. A says that the car is moving in east direction and B says that 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

• A. $\theta =ta{n}^{-1}\left(\frac{1}{2}\right)$ North of East
• B. $\theta =ta{n}^{-1}\left(\frac{1}{2}\right)$ South of East
• C. $\theta =ta{n}^{-1}\left(2\right)$ North of East
• D. none of these

Answer 1

The correct option is B $\theta =ta{n}^{-1}\left(\frac{1}{2}\right)$ South of East

Relative velocity,
$V_C-V_A=V\hat{i}$
$V_C-2V_A=V\hat{j}$
Equating both we get,
$V_C=V(2\hat{i}-\hat{j})$
$\therefore tan\theta =\frac{-1}{2}$
i.e. in south east direction.