Question

Two trains $121\, m$ and $99 \,m$ in length are running in opposite directions with velocities $40 \,km \,h^{-1}$ and $32\,km\,h^{-1}$. In what time they will completely cross each other ?

• A. $9\,s$
• B. $11\,s$
• C. $13\,s$
• D. $15\,s$

Answer 1

Answer: (B)

Here, $v_A = 40\, km\, h ^{-1}, v_B = -32\, km\, h^{-1}$
Length of train $A, l_A = 121\, m$
Length of train $B, l_B = 99 \,m$
Relative velocity of two trains is given by
$v_{AB} = v_A - v_B = 40 - (-32)$
$ = 72 \,km\,h^{-1} $
$ = 72 \times \frac{5}{18} = 20 \, m \, s^{-1}$
Total distance to be travelled by each train for completely crossing the other train
$= 121 + 99 = 220\, m$
$\therefore $ Time taken by each train to cross the other train
$= \frac{220}{20} = 11\,s$
Hence the two trains will cross each other in $11\, s$.