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A 120 m120 \text{ m} long train is moving in a direction with speed 20 m/s20 \text{ m/s}. A train B moving with 30 m/s30 \text{ m/s} in the opposite direction and 130 m130 \text{ m} long crosses the first train in a time:

A

4 s

B

36 s

C

38 s

D

5 s

Step-by-Step Solution

  1. Concept - Relative Velocity: When two objects move in opposite directions, their relative velocity is the sum of their individual speeds.
  • vrelative=vA+vB=20 m/s+30 m/s=50 m/sv_{relative} = v_A + v_B = 20 \text{ m/s} + 30 \text{ m/s} = 50 \text{ m/s} .
  1. Total Distance: For the two trains to cross each other completely, the total distance to be covered is the sum of their lengths.
  • d=LA+LB=120 m+130 m=250 md = L_A + L_B = 120 \text{ m} + 130 \text{ m} = 250 \text{ m}.
  1. Calculate Time: The time taken to cross is the total distance divided by the relative speed.
  • t=dvrelative=25050=5 st = \frac{d}{v_{relative}} = \frac{250}{50} = 5 \text{ s}.
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