Master the logic of self-length and relative distance. Learn how to solve complex crossing scenarios involving platforms, bridges, and moving observers.
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1. The Fundamental Crossing Law
Distance covered during crossing is the SUM of lengths involved.
Crossing a Pole/Man: Distance = Length of Train (L_1).
Crossing a Platform/Bridge: Distance = Length of Train + Length of Platform (L_1 + L_2).
Example:
Q: A 200m train crosses a pole in 10s. Speed?
Solution: Speed = 20010 = 20 m/s = 72 kmph.
2. Relative Speed in Trains
When two trains cross each other.
Total Distance: ALWAYS L_1 + L_2 (Lengths never subtract).
Relative Speed (Opposite): S_1 + S_2.
Relative Speed (Same): S_1 - S_2.
Example:
Q: Two trains (150m, 250m) at 40 kmph and 50 kmph (Opposite). Time?
Solution: Total Dist = 400m. Rel Speed = 90 kmph = 25 m/s. Time = 40025 = 16 sec.
3. Point Observer in a Moving Train
When a faster train crosses a Man sitting in a slower train.
The Model: Treat the Man as a point object moving at the speed of the slower train.
Logic: Distance = ONLY the length of the Faster Train (L_{fast}).
The length of the slower train is IRRELEVANT.
Example:
Q: Fast train (200m) crosses a man in slow train in 10s. Rel Speed?