A passenger sitting in a train A moving at 90 km/h observes another train B moving in the opposite direction for 8 s. If the velocity of the train B is 54 km/h, then length of train B is [2023]

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Solution

Q.
A passenger sitting in a train A moving at 90 km/h observes another train B moving in the opposite direction for 8 s. If the velocity of the train B is 54 km/h, then length of train B is [2023]

1 80 m

2 200 m

3 120 m

4 320 m

Ans.
(4)

Velocity of train A

$V_{A} = 90 \frac{km}{hr} = 90 \times \frac{5}{18} = 25 m/s$

Velocity of train B

$V_{B} = 54 \frac{km}{hr} = 54 \times \frac{5}{18} = 15 m/s$

Velocity of train B w.r.t. train A $= {\vec{V}}_{B} - {\vec{V}}_{A}$

$= 15 - (- 25) m/s = 40 m/s$

$Time of crossing = \frac{length of train}{relative velocity}$

$8 = \frac{ℓ}{40}$

$\Rightarrow l = 8 \times 40 = 320 meter$

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