Question

A train moves northwards with speed $80km{h}^{-1}$, while a car moves towards east with a speed of $60km{h}^{-1}$. What is the velocity of the train w.r.t the driver of the car?

Answer 1

Let the east direction be along $\hat{i}$ and north direction be along $\hat{j}$.

Then , the velocity of train, ${\overrightarrow{v}}_{train}$ = $80$ $km{h}^{-1}$ $\hat{j}$

Velocity of car, ${\overrightarrow{v}}_{car}$ = $60$ $km{h}^{-1}$ $\hat{i}$

Therefore , velovity of the train w.r.t the driver of the car = ${\overrightarrow{v}}_{train}$ - ${\overrightarrow{v}}_{car}$

= $80$ $km{h}^{-1}$ $\hat{j}$ - $60$ $km{h}^{-1}$ $\hat{i}$