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Question 2

Train A is moving along two parallel rail tracks towards north with $$72 \text{ km h}^{-1}$$ and train B is moving towards south with speed $$108 \text{ km h}^{-1}$$. Velocity of train B with respect to A and velocity of ground with respect to B are (in $$\text{m s}^{-1}$$):

First, convert the speeds from km/h to m/s using the conversion factor: $$1 \text{ km/h} = \frac{5}{18} \text{ m/s}$$.

For Train A moving north:
Speed $$v_A = 72 \text{ km/h} = 72 \times \frac{5}{18} = 20 \text{ m/s}$$ (north direction).

For Train B moving south:
Speed $$v_B = 108 \text{ km/h} = 108 \times \frac{5}{18} = 30 \text{ m/s}$$ (south direction).

Assign directions: Let north be positive and south be negative.
Thus, $$v_A = +20 \text{ m/s}$$ and $$v_B = -30 \text{ m/s}$$.

Velocity of train B with respect to A ($$v_{BA}$$):
The relative velocity formula is $$v_{BA} = v_B - v_A$$.
Substitute values: $$v_{BA} = (-30) - (20) = -50 \text{ m/s}$$.

Velocity of ground with respect to B ($$v_{GB}$$):
The ground is stationary, so $$v_G = 0 \text{ m/s}$$.
The relative velocity formula is $$v_{GB} = v_G - v_B$$.
Substitute values: $$v_{GB} = 0 - (-30) = +30 \text{ m/s}$$.

Therefore, the velocities are $$-50 \text{ m/s}$$ and $$30 \text{ m/s}$$, which corresponds to option C.

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