Two parallel rail tracks run north-south. On one track train $A$ moves north with a speed of $54 \ma

Question

Two parallel rail tracks run north-south. On one track train $A$ moves north with a speed of $54 \mathrm{~km} \mathrm{~h}^{-1}$ and on the other track train $B$ moves south with a speed of $90 \mathrm{~km} \mathrm{~h}^{-1}$. The velocity (in $\mathrm{m} \mathrm{s}^{-1}$ ) of $\operatorname{train} A$ with respect to train $B$ is

Professor PC Thomas Classes · Answer

(d) : Let the positive direction of motion be from south to north. Velocity of $\operatorname{train} A$ with respect to ground
$v_{A G}=+54 \mathrm{~km} \mathrm{~h}^{-1}=+54 	imes \frac{5}{18} \mathrm{~m} \mathrm{~s}^{-1}$\ $=+15 \mathrm{~m} \mathrm{~s}^{-1}$
Velocity of train $B$ with respect to ground $v_{B G}=-90 \mathrm{~km} \mathrm{~h}^{-1}=-90 	imes \frac{5}{18} \mathrm{~m} \mathrm{~s}^{-1}=-25 \mathrm{~m} \mathrm{~s}^{-1}$\ Relative velocity of train $A$ with respect to train $B$ is 
$v_{A B}=v_{A G}+v_{G B}=v_{A G}-v_{B G} \quad\left(\because v_{G B}=-v_{B G}ight)$\ $=+15 \mathrm{~m} \mathrm{~s}^{-1}-\left(-25 \mathrm{~m} \mathrm{~s}^{-1}ight)=40 \mathrm{~m} \mathrm{~s}^{-1}$