Question

A man is going east in a car with a velocity of $(20\, km / hr )$, 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. $40\, m / s , 60^{\circ} N$ of $W$
• B. $40\, m / s , 60^{\circ} W$ of $N$
• C. $40\, m / s , 60^{\circ} N$ of $E$
• D. $40\, m / s , 60^{\circ} E$ of $N$

Answer 1

Answer: (C)

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