Question

Train $A$ and train $B$ are running on parallel tracks in the opposite directions with speeds of $36{\text{km h}}^{-1}$ and $72{\text{km h}}^{-1}$, respectively. A person is walking in train $A$ in the direction opposite to its motion with a speed of $1.8{\text{km h}}^{-1}$. The speed $\left({\text{in ms}}^{–1}\right)$ of this person as observed from train $B$ will be close to

• A. $29.5{\text{ms}}^{-1}$
• B. $28.5{\text{ms}}^{-1}$
• C. $31.5{\text{ms}}^{-1}$
• D. $30.5{\text{ms}}^{-1}$

Answer 1

The correct option is A $29.5{\text{ms}}^{-1}$

According to the question, train $A$ and $B$ are running on parallel tracks in the opposite direction.




$V_A=36{\text{km h}}^{-1}=10{\text{ms}}^{-1}$
$V_B=-72{\text{km h}}^{-1}=-20{\text{ms}}^{-1}$
$V_{man,A}=-1.8{\text{km h}}^{-1}=-0.5{\text{ms}}^{-1}$

$V_{\text{man,B}}=V_{\text{man,A}}+V_{A.B}$

$\Rightarrow V_{\text{man,B}}=V_{\text{man,A}}+V_A-V_B$

$\Rightarrow V_{\text{man,B}}=-0.5+10-(-20)$

$\Rightarrow V_{\text{man,B}}=-0.5+30=29.5{\text{ms}}^{-1}$.

Hence, option $\left(A\right)$ is correct.