A passenger sitting in a train A moving at $90 \mathrm{~km} / \mathrm{h}$ observes another train $\mathrm{B}$ moving in the opposite direction for $8 \mathrm{~s}$. If the velocity of the train B is $54 \mathrm{~km} / \mathrm{h}$, then length of train B is:

To find the length of train B, we first need to determine the relative velocity between train A and train B. Since they are moving in opposite directions, their velocities add up: <br/><br/> $v_{AB} = v_A + v_B = 90 \mathrm{~km/h} + 54 \mathrm{~km/h} = 144 \mathrm{~km/h}$ <br/><br/> Now, we need to convert this relative velocity to meters per second: <br/><br/> $$v_{AB} = \frac{144 \mathrm{~km/h} × 1000 \mathrm{~m/km}}{3600 \mathrm{~s/h}} = 40 \mathrm{~m/s}$$ <br/><br/> The passenger in train A observes train B for 8 seconds. To find the length of train B, we can use the formula: <br/><br/> $\text{length} = \text{relative velocity} × \text{time}$ <br/><br/> $\text{length} = 40 \mathrm{~m/s} ~×~ 8 \mathrm{~s} = 320 \mathrm{~m}$ <br/><br/> So, the length of train B is 320 meters.