दो ट्रेनें विपरीत दिशा में 48 km/hr और 60 km/hr की गति से चल रही हैं। धीमी ट्रेन द्वारा तेज ट्रेन में बैठे व्यक्ति को पार करने में 12 सेकंड का समय लगता है। धीमी ट्रेन की लंबाई क्या... दो ट्रेनें विपरीत दिशा में 48 km/hr और 60 km/hr की गति से चल रही हैं। धीमी ट्रेन द्वारा तेज ट्रेन में बैठे व्यक्ति को पार करने में 12 सेकंड का समय लगता है। धीमी ट्रेन की लंबाई क्या है?
Understand the Problem
प्रश्न में दो ट्रेनों के गति, समय और एक यात्री द्वारा पार किए गए समय की सहायता से धीमी ट्रेन की लंबाई ज्ञात करने के लिए पूछा गया है।
Answer
The length of the slower train is $360 \text{ m}$.
Answer for screen readers
The length of the slower train is $360 \text{ m}$.
Steps to Solve
- Convert train speeds to the same unit
The speeds of the trains are given in kilometers per hour (km/hr). To make calculations easier, we can convert these speeds to meters per second (m/s).
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Speed of slower train: $$ 48 \text{ km/hr} = \frac{48 \times 1000}{3600} = \frac{48000}{3600} = \frac{480}{36} = \frac{40}{3} \text{ m/s} $$
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Speed of faster train: $$ 60 \text{ km/hr} = \frac{60 \times 1000}{3600} = \frac{60000}{3600} = \frac{600}{36} = \frac{50}{3} \text{ m/s} $$
- Calculate the relative speed of the trains
Since the trains are moving in opposite directions, their speeds will add up.
- Relative speed: $$ \text{Relative speed} = \left(\frac{40}{3} + \frac{50}{3}\right) = \frac{90}{3} = 30 \text{ m/s} $$
- Determine the distance covered by the slower train
The time taken by the slower train to cross a man sitting in the faster train is given as 12 seconds.
- Distance: $$ \text{Distance} = \text{Relative speed} \times \text{Time} $$ $$ \text{Distance} = 30 \text{ m/s} \times 12 \text{ s} = 360 \text{ m} $$
- Determine the length of the slower train
Since the distance covered includes the length of the slower train, we can conclude that the length of the slower train is 360 meters.
The length of the slower train is $360 \text{ m}$.
More Information
In this problem, we utilized the concept of relative speed, which becomes important when two objects move in opposite directions. Knowing how to convert units between km/hr and m/s also aids in solving distance-based problems in physics.
Tips
- Mistake in unit conversion: Failing to correctly convert the speed from km/hr to m/s can lead to incorrect calculations. Always double-check the conversion.
- Ignoring relative speed: When two objects move in opposite directions, ignoring the addition of their speeds will result in an incorrect answer.
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