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 Concept:
When two objects move relative to each other, we use the concept of relative velocity. If they move in opposite directions, their relative speed is the sum of their individual speeds. The passenger in train A sees train B cover its own length at this relative speed.
Step 2: Key Formula or Approach:
1. Relative velocity ($v_{rel}$) = $v_A + v_B$ (for opposite directions).
2. Length of train B ($L$) = $v_{rel} \times \text{time}$.
Step 3: Detailed Explanation:
1. Convert velocities to m/s: \[ v_A = 90 \times \frac{5}{18} = 25 \, \text{m/s} \] \[ v_B = 54 \times \frac{5}{18} = 15 \, \text{m/s} \]
2. Calculate Relative Velocity: \[ v_{rel} = 25 + 15 = 40 \, \text{m/s} \]
3. Calculate Length: \[ L = 40 \, \text{m/s} \times 8 \, \text{s} = 320 \, \text{m} \]
Step 4: Final Answer
The length of train B is 320 m.