Question

A man is going east in a car with a velocity of $(20km/hr)$, a train appears to move towards north to him with a velocity of $20\sqrt{3}km/hr$. What is the actual velocity and direction of motion of train?

• A. $40m/s,60^{\circ }N$ of $W$
• B. $40m/s,60^{\circ }W$ of $N$
• C. $40m/s,60^{\circ }N$ of $E$
• D. $40m/s,60^{\circ }E$ of $N$

Answer 1

Answer: (C)

$v_C=20km/hr$ EAST
$v_{TC}=20\sqrt{3}km/hr$ NORTH
${\vec{v}}_{TC}={\vec{v}}_T-{\vec{v}}_C$
${\vec{v}}_T={\vec{v}}_{TC}+{\vec{v}}_C$
${\vec{v}}_T=20\sqrt{3}\hat{j}+20\hat{i}$
$\left|{\vec{v}}_T\right|=\sqrt{1200+400}=40m/s$
$\tan \theta =\frac{20\sqrt{3}}{20}$
$\tan \theta =\sqrt{3}$
$\theta =60^{\circ }$