Two Trains & Moving Observers
दो trains और चलता-फिरता observer
Two Trains & Moving Observers
- Problems on Trains
- Two Trains & Moving Observers
Combine relative speed with lengths for two trains, or a man moving inside or beside a train.
🎯 Learning Objective
Combine relative speed with lengths for two trains, or a man moving inside or beside a train.
💡 Concept
- Two trains crossing each other: distance = L₁ + L₂, always
- Opposite directions → divide by (v₁ + v₂); same direction → divide by (v₁ − v₂)
- A running man or a passenger in another train is a POINT → only the crossing train's length counts
- Add or subtract speeds in km/h first, convert the single result to m/s
🧮 Key Formulas
Opposite: t = (L₁ + L₂)/(v₁ + v₂)
>
Same: t = (L₁ + L₂)/(v₁ − v₂)
>
Moving man: distance = train's length only
✏️ Easy Example
Q. Two trains 120 m and 80 m long run towards each other at 30 km/h and 42 km/h. In how many seconds do they cross each other?
- Relative = 30 + 42 = 72 km/h = 20 m/s
- Distance = 120 + 80 = 200 m
- 200 ÷ 20 = 10
Answer: 10 seconds
🇮🇳 Real-Life Example
From a Rajdhani window, an oncoming express flashes past in seconds, but an overtaken goods train crawls beside you forever — sum versus difference of speeds, felt from your seat.
📝 Exam-Level Example
Q. Two trains 100 m and 120 m long run in the same direction at 72 km/h and 54 km/h. How long does the faster train take to completely overtake the slower one?
- Relative = 72 − 54 = 18 km/h = 5 m/s
- Distance = 100 + 120 = 220 m
- 220 ÷ 5 = 44
Answer: 44 seconds
📝 Exam-Level Example
Q. A 110 m long train moving at 60 km/h passes a man running at 6 km/h in the opposite direction. In how much time does it pass him?
- Relative = 60 + 6 = 66 km/h = 55/3 m/s
- Time = 110 ÷ (55/3) = 110 × 3/55
- = 6
Answer: 6 seconds
🪄 Memory Trick
Ask one question — WHO has length? Trains yes; men, poles and passengers no. Add the lengths of everything that does.
⚠️ Common Mistakes
- ❌ Giving the running man a 'length'
- ❌ Adding speeds for same-direction overtaking (subtract them)
- ❌ Converting each speed separately and rounding — combine in km/h first
🏆 Exam Tips
- ✅ Same-direction crossing takes LONGER — small relative speed
- ✅ Man running opposite to the train → his speed adds to the train's
📌 Summary
- Two trains → L₁ + L₂ over relative speed
- Opposite add, same direction subtract
- Moving man = point, only train's length
- Combine speeds in km/h, convert once