Question

Two trains are moving on parallel tracks in opposite directions at the speeds of $20\text{m/s}$ and $15\text{m/s}$ respectively. If both the trains are of equal length $140\text{m}$ each, then how much time will they take to cross each other?

• A. $4\text{s}$
• B. $8\text{s}$
• C. $16\text{s}$
• D. $2\text{s}$

Answer 1

The correct option is B $8\text{s}$

As both trains are moving in opposite direction the relative velocity of train $1$ with respect to train $2$ will be:
$\Rightarrow v_{rel}=v_{12}=v_1-(-v_2)=v_1+v_2$
$\Rightarrow v_{12}=20+15=35\text{m/s}$

Here, the displacement of train ($1$) from frame of reference of train ($2$) , when both trains cross each other will be equal to sum of length of both trains:
$\Rightarrow l=l_1+l_2$
Or, $l=140+140$
$\therefore l=280\text{m}$
$\therefore$ Total time required to cross each other :
$\Rightarrow t=\frac{l}{v_{12}}=\frac{l_1+l_2}{v_{12}}$
$\therefore t=\frac{280}{35}=8\text{s}.$