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

Hint:

Note that we only use the length of the train that is being "observed" passing a "point passenger". We don't add the length of train A because the passenger is a single point observer.

Answer 1

Step 1: Understanding the Question:
The passenger in train A sees the entirety of train B pass by. We need to find the length of train B using the relative speed and time of observation.

Step 2: Key Formula or Approach:
1. For opposite directions, Relative Velocity \(V_{rel} = V_A + V_B\).
2. Convert km/h to m/s by multiplying with \(\frac{5}{18}\).
3. Distance (Length of train B) = \(V_{rel} \times \text{time}\).

Step 3: Detailed Explanation:
Velocity of Train A, \(V_A = 90 \times \frac{5}{18} = 25 \text{ m/s}\).
Velocity of Train B, \(V_B = 54 \times \frac{5}{18} = 15 \text{ m/s}\).
Since they move in opposite directions, relative velocity of B with respect to A:
\[ V_{rel} = 25 + 15 = 40 \text{ m/s} \] The passenger sees train B for 8 seconds. In this time, the entire length of train B passes the passenger.
Length of Train B = \(40 \text{ m/s} \times 8 \text{ s} = 320 \text{ m}\).

Step 4: Final Answer:
The length of train B is 320 m.