First slide

Relative velocity in 1-d

Question

A passenger train of length 60 m travels at a speed of $80 k m / h r$ . Another freight train of length 120 m travels at a speed of $30 k m / h r$ . The ratio of times taken by the passenger train to completely cross the freight train when
i) They are moving in the same direction
ii) In the opposite direction is

Moderate

A

$\frac{25}{11}$
B

$\frac{3}{2}$
C

$\frac{11}{5}$
D

$\frac{5}{2}$

Solution

$\overset{60 m}{\to} 80 k m / h r$
$\underset{120 m}{\to} 30 k m / h r$
Relative speed of passenger train $= v_{1} - v_{2} = 50 k m / h r$
$T_{1} = \frac{t o t a l l e n g t h o f t r a i n =}{r e l a t i v e s p p e d} \frac{180}{50}$
Trains are moving in opposite direction
Relative speed of train $= v_{1} + v_{2} = 110 k m / h r$
$T_{2} = \frac{t o t a l l e n g t h o f t r a i n =}{r e l a t i v e s p e e d} \frac{180}{110}$
$\frac{T_{1}}{T_{2}} = \frac{110}{50} = \frac{11}{5}$

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