Question

A train move eastward with speed $72kmph$ while a car moves towards west with speed of $54kmph$. Then magnitude of velocity of car with respect to an observer sitting in train is:

• A. $10m/s$
• B. $35m/s$
• C. $35km/h$
• D. $10km/h$

Answer 1

The correct option is B $35m/s$

Take, east direction $\hat{i}$ and west direction $-\hat{i}$

Velocity of car and train, $V_c=54(-\hat{i})kmphand{V}_t=72\hat{i}kmph$

Relative velocity of car with respect to train,

$V_{ct}=V_c-V_t=-54\hat{i}-72\hat{i}=-126\hat{i}$

$\left|V_{ct}\right|=126kmph=126\times \frac{5}{18}=35m{s}^{-1}$

Hence, magnitude of velocity of car with respect to person sit in train is $35m{s}^{-1}$