JEE MAIN - Physics (2023 - 13th April Evening Shift - No. 18)
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:
80 m
200 m
120 m
320 m
Explanation
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:
$$v_{AB} = v_A + v_B = 90 \mathrm{~km/h} + 54 \mathrm{~km/h} = 144 \mathrm{~km/h}$$
Now, we need to convert this relative velocity to meters per second:
$$v_{AB} = \frac{144 \mathrm{~km/h} × 1000 \mathrm{~m/km}}{3600 \mathrm{~s/h}} = 40 \mathrm{~m/s}$$
The passenger in train A observes train B for 8 seconds. To find the length of train B, we can use the formula:
$$\text{length} = \text{relative velocity} × \text{time}$$
$$\text{length} = 40 \mathrm{~m/s} ~×~ 8 \mathrm{~s} = 320 \mathrm{~m}$$
So, the length of train B is 320 meters.
$$v_{AB} = v_A + v_B = 90 \mathrm{~km/h} + 54 \mathrm{~km/h} = 144 \mathrm{~km/h}$$
Now, we need to convert this relative velocity to meters per second:
$$v_{AB} = \frac{144 \mathrm{~km/h} × 1000 \mathrm{~m/km}}{3600 \mathrm{~s/h}} = 40 \mathrm{~m/s}$$
The passenger in train A observes train B for 8 seconds. To find the length of train B, we can use the formula:
$$\text{length} = \text{relative velocity} × \text{time}$$
$$\text{length} = 40 \mathrm{~m/s} ~×~ 8 \mathrm{~s} = 320 \mathrm{~m}$$
So, the length of train B is 320 meters.
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