Question

Train A is moving along two parallel rail tracks towards north with speed 72 km/h and train B is moving towards south with speed 108 km/h.Velocity of train B with respect to A and velocity of ground with respect to B are (in m/s) :

• A. –30 and 50
• B. –50 and –30
• C. –50 and 30
• D. 50 and –30

Answer 1

The Correct Option is C

To determine the velocity of train B relative to train A and the velocity of the ground relative to train B, follow these steps:

1. Convert speeds from km/h to m/s:
   • Speed of train A, \( V_A = 72 \, \text{km/h} \). Conversion factor: \( \frac{5}{18} \).
   • \(V_A = 72 \times \frac{5}{18} = 20 \, \text{m/s}\).
   • Speed of train B, \( V_B = 108 \, \text{km/h} \):
   • \(V_B = 108 \times \frac{5}{18} = 30 \, \text{m/s}\).
2. Calculate the velocity of train B with respect to train A:
   • Relative velocity formula: \( V_{\text{relative}} = V_{\text{object}} - V_{\text{reference}} \).
   • As train B moves in the opposite direction of train A:
   • \(V_{BA} = V_B - (-V_A) = V_B + V_A = 30 + 20 = 50 \, \text{m/s}\).
   • Considering the opposite direction of motion for B relative to A:
   • \(V_{BA} = -50 \, \text{m/s}\).
3. Calculate the velocity of the ground with respect to train B:
   • The ground's absolute velocity is 0 m/s. From train B's frame of reference, the ground appears to move in the direction opposite to B.
   • Velocity of the ground with respect to train B:
   • \(V_{\text{ground, B}} = 0 - (-V_B) = V_B = 30 \, \text{m/s}\).

Thus, the velocity of train B relative to train A is \(-50 \, \text{m/s}\), and the velocity of the ground relative to train B is \(30 \, \text{m/s}\).

Correct Answer: –50 and 30