Question

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

• A. 80 m
• B. 200 m
• C. 120 m
• D. 320 m

Answer 1

Answer: (D)

320 m

Answer 2

1. Convert velocities to m/s:

   • Velocity of train A, $V_A = 90 \text{ km/h}$ $V_A = 90 \times \frac{5}{18} \text{ m/s} = 5 \times 5 \text{ m/s} = 25 \text{ m/s}$
   • Velocity of train B, $V_B = 54 \text{ km/h}$ $V_B = 54 \times \frac{5}{18} \text{ m/s} = 3 \times 5 \text{ m/s} = 15 \text{ m/s}$

2. Calculate relative velocity:

   Since the trains are moving in opposite directions, their relative velocity is the sum of their individual velocities. $V_{\text{rel}} = V_A + V_B$ $V_{\text{rel}} = 25 \text{ m/s} + 15 \text{ m/s} = 40 \text{ m/s}$

3. Calculate the length of train B:

   The length of train B is the distance covered by train B relative to train A during the observation time. Length of train B, $L_B = V_{\text{rel}} \times t$ $L_B = 40 \text{ m/s} \times 8 \text{ s}$ $L_B = 320 \text{ m}$