Question

A line AB is making an angle of ${30}^{\circ }$ from +ve x-axis, the line is in xy plane, what is the velocity of a car moving with speed 36 $km/hr$ along AB?

• A. $(36\sqrt{3}\hat{i}+36\hat{j})m/s$
• B. $(5\hat{i}+5\sqrt{3}\hat{j})m/s$
• C. $(5\sqrt{3}\hat{i}+5\hat{j})m/s$
• D. $(10\sqrt{3}\hat{i}+10\hat{j})m/s$

Answer 1

The correct option is C $(5\sqrt{3}\hat{i}+5\hat{j})m/s$

velocity = speed X {unit vector}
$\overrightarrow{AB}=cos30\hat{i}+sin30\hat{j}=\sqrt{3}/2\hat{i}+1/2\hat{j}=\frac{(\sqrt{3}\hat{i}+\hat{j})}{2}m/s$
(it is already a unit vector)
velocity = speed {unit vector}
= 10 m/s $\left\{\frac{\sqrt{3}\hat{i}+\hat{j}}{2}\right\}=5\sqrt{3}\hat{i}+5\hat{j}m/s$