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 ms⁻¹):

Solution

Physics sir · 4 steps

Fix north as positive, and each relative velocity becomes one clean subtraction.

1. Convert and sign. Multiply by 5/18 to convert to m s⁻¹, and take north as positive. Then v_A = 72 × 5/18 = +20 m s⁻¹ and v_B = -108 × 5/18 = -30 m s⁻¹.

   v⃗_(BA) = v⃗_B - v⃗_A

2. B relative to A. v_(BA) = -30 - 20 = -50 m s⁻¹. To a passenger in A, train B rushes south at 50 m s⁻¹.
3. Ground relative to B. The ground has velocity 0, so v_(GB) = 0 - (-30) = +30 m s⁻¹. To a passenger in B, the ground slides north.
4. So. The two velocities are -50 and 30 m s⁻¹, which is option (b).

The idea to keep. Velocity of X with respect to Y is always v_X - v_Y. Fix one positive direction first, and the signs take care of themselves.

Answer from the NTA final answer key. Solution by PrepWiser.