Question

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 train B is 54 km/h, then the length of train B is:

• A. 100 m
• B. 320 m
• C. 200 m
• D. 400 m

Answer 1

The Correct Option is B

The velocity of train A (\( V_A \)) is given as \( 90 \, \text{km/h} \), which can be converted to SI units: \[ V_A = 90 \, \text{km/h} = 25 \, \text{m/s}. \] The velocity of train B (\( V_B \)) is given as \( 54 \, \text{km/h} \): \[ V_B = 54 \, \text{km/h} = 15 \, \text{m/s}. \] Since the trains are moving in opposite directions, the relative velocity (\( V_{BA} \)) is the sum of their velocities: \[ V_{BA} = V_A + V_B = 25 \, \text{m/s} + 15 \, \text{m/s} = 40 \, \text{m/s}. \] The time of crossing (\( t \)) is given as \( 8 \, \text{s} \). The length of train B (\( \ell \)) is related to the time of crossing and relative velocity as: \[ t = \frac{\ell}{V_{BA}}. \] Substituting the values: \[ 8 = \frac{\ell}{40}. \] Solving for \( \ell \): \[ \ell = 8 \times 40 = 320 \, \text{m}. \] Thus, the length of train B is \( \boxed{320 \, \text{m}} \).